<PAGE>   1
                                    FORM 10-Q

                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

[X]               QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE
                  SECURITIES EXCHANGE ACT OF 1934

                For the quarterly period ended September 30, 1998

                                      OR

[ ]               TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE
                         SECURITIES EXCHANGE ACT OF 1934

          For the transition period from ____________ to _____________

                          Commission file number 1-8971

                                   RCPI Trust
             (Exact name of registrant as specified in its charter)

              Delaware                                    13-7087445 
(State or other jurisdiction of                        (I.R.S. Employer
 incorporation or organization)                       Identification No.)

                       c/o Tishman Speyer Properties, L.P.
                   45 Rockefeller Plaza, New York, N.Y. 10011
               (Address of principal executive offices) (Zip Code)


                                 (212) 332-6500
              (Registrant's telephone number, including area code)

                     --------------------------------------
              (Former name, former address, and former fiscal year,
                          if changed since last report)

Indicate by check mark whether the registrant (1) has filed all reports required
to be filed by Section 13 or 15(d) of the Securities Exchange Act of 1934 during
the preceding 12 months (or for such shorter period that the registrant was
required to file such reports), and (2) has been subject to such filing
requirements for the past 90 days.

Yes    X    No
    ------     ------


<PAGE>   2
                                   RCPI TRUST


INDEX


<TABLE>
<CAPTION>
                                                                                          PAGE
                                                                                          ----
<S>                                                                                      <C>
PART I--FINANCIAL INFORMATION

ITEM 1.     FINANCIAL STATEMENTS

The accompanying unaudited, interim financial statements have been prepared in
accordance with the instructions to Form 10-Q. In the opinion of management, all
adjustments necessary for a fair presentation have been included.

            RCPI Trust,  Balance  Sheets as of September 30, 1998  (unaudited)
            and December 31, 1997                                                          1

            RCPI Trust, Statements of Operations for the quarters ended September 30,
            1998 and 1997 (unaudited) and for the nine months ended September 30,
            1998 and 1997 (unaudited)                                                      2

            RCPI Trust,  Statements  of Cash Flows for the nine  months  ended
            September 30, 1998 and 1997 (unaudited)                                        3

            Notes to Financial Statements (unaudited)                                      4


ITEM 2.     MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND
            RESULTS OF OPERATIONS                                                          5


PART II--OTHER INFORMATION


ITEM 1.     LEGAL PROCEEDINGS                                                              8

ITEM 6.     EXHIBITS AND REPORTS ON FORM 8-K                                               9
</TABLE>
<PAGE>   3

PART I -- FINANCIAL INFORMATION
  ITEM 1.  Financial Statements

                                   RCPI TRUST
                          (A Delaware business trust)
                                 BALANCE SHEETS
                                ($ in thousands)


<TABLE>
<CAPTION>
                                                                                  As of                As of
                                                                             Sept. 30, 1998         December 31,
                                                                               (Unaudited)             1997
                                                                               -----------             ----
<S>                                                                          <C>                    <C>
ASSETS:

Real Estate:
  Land                                                                          $ 158,149           $ 158,149
  Buildings and improvements                                                      626,930             611,711
  Tenant improvements                                                              46,957              36,170
  Furniture, fixtures and equipment                                                 4,564               4,192
                                                                                ---------           ---------
                                                                                  836,600             810,222
     Less:  Accumulated depreciation and amortization                             (38,964)            (24,393)
                                                                                ---------           ---------
                                                                                  797,636             785,829

Cash and cash equivalents                                                          35,585              27,517
Restricted cash                                                                     9,656               9,369
Accounts receivable                                                                 5,815              11,946
Prepaid expenses                                                                    9,576                 495
Deferred costs, net of accumulated
  amortization of $4,735 and $2,192, respectively                                  36,524              22,521
Accrued rent                                                                       58,829              29,969
                                                                                ---------           ---------
  Total Assets                                                                  $ 953,621           $ 887,646
                                                                                =========           =========

LIABILITIES AND OWNERS' EQUITY

Liabilities:
Zero coupon convertible debentures, net of unamortized
   discount of $139,095 and $177,696, respectively                              $ 447,090           $ 408,489
14% debentures (includes premium of $23,540 and $24,710, respectively)             98,540              99,710
NationsBank loans                                                                  85,000              55,000
Accrued interest payable                                                            2,037               7,152
Accounts payable and accrued expenses                                              16,365              21,227
Tenant security deposits payable                                                    9,731               8,940
                                                                                ---------           ---------
  Total Liabilities                                                               658,763             600,518

Commitments and Contingencies

Owners' Equity                                                                    294,858             287,128
                                                                                ---------           ---------
  Total Liabilities and Owners' Equity                                          $ 953,621           $ 887,646
                                                                                =========           =========
</TABLE>

                     SEE NOTES TO THE FINANCIAL STATEMENTS

                                       1
<PAGE>   4
                                   RCPI TRUST
                          (A Delaware business trust)
                            STATEMENTS OF OPERATIONS
                                ($ in thousands)
                                  (UNAUDITED)


<TABLE>
<CAPTION>
                                                          For the Quarters Ended              For the Nine Months Ended
                                                               September 30,                        September 30,
                                                          1998               1997              1998               1997
                                                          ----               ----              ----               ----
<S>                                                     <C>               <C>                <C>               <C>
Revenues:
    Base rental                                         $ 48,243          $ 42,321           $143,052          $125,783
    Operating escalations and percentage rents             1,815             1,995              5,159             5,376
    Interest and other income                              2,105             1,865              5,382             7,077
                                                        --------          --------           --------          --------
        Total revenues                                    52,163            46,181            153,593           138,236
                                                        --------          --------           --------          --------

Expenses:
    Interest                                              17,173            15,494             49,265            43,578
    Real estate taxes                                      8,657             8,562             25,486            25,030
    Payroll and benefits                                   4,972             4,240             15,052            13,302
    Repairs, maintenance and supplies                      3,543             3,068             10,448             8,460
    Utilities                                              4,211             4,753             10,248            12,593
    Cleaning                                               3,267             3,435             10,134            10,291
    Professional fees                                        196               641              1,003             4,883
    Insurance                                                235               315                812               914
    Management and accounting fees                           888               812              2,646             2,516
    General and administration                             1,094             1,212              3,251             2,101
    Depreciation and amortization                          6,194             5,124             17,518            14,330
                                                        --------          --------           --------          --------
        Total expenses                                    50,430            47,656            145,863           137,998
                                                        --------          --------           --------          --------
Net income (loss)                                       $  1,733          ($ 1,475)          $  7,730          $    238
                                                        ========          ========           ========          ========
</TABLE>

                     SEE NOTES TO THE FINANCIAL STATEMENTS

                                       2
<PAGE>   5
                                   RCPI TRUST
                          (A Delaware business trust)
                            STATEMENTS OF CASH FLOWS
                                ($ in thousands)
                                  (UNAUDITED)


<TABLE>
<CAPTION>
                                                                 For the Nine Months Ended
                                                                        September 30,
                                                                   1998               1997
                                                                   ----               ----
<S>                                                              <C>                <C>
Cash Flows from Operating Activities:
   Net income                                                    $  7,730           $    238
   Adjustment to reconcile net income to net cash
    provided by operating activities:
    Amortization of original issue discount and premium            37,431             33,154
    Depreciation and amortization                                  17,518             14,330
    (Increase) decrease in restricted cash                           (287)               924
    Decrease in accounts receivable                                 6,131              9,778
    Increase in prepaid expenses                                   (9,081)            (8,908)
    Increase in accrued rent                                      (28,860)           (12,157)
    Decrease in accounts payable and accrued expenses
      and tenant security deposits payable                         (1,209)            (5,031)
    Decrease in accrued interest payable                           (5,114)            (1,667)
                                                                 --------           --------
       Net cash provided by operating activities                   24,259             30,661
                                                                 --------           --------

Cash Flows from Investing Activities:
    Additions to building and improvements                        (15,416)            (9,398)
    Additions to tenant improvements                              (15,274)           (10,443)
    Additions to furniture, fixtures and equipment                   (372)               (86)
    Additions to deferred costs                                   (15,129)           (12,868)
                                                                 --------           --------
       Net cash used in investing activities                      (46,191)           (32,795)
                                                                 --------           --------

Cash Flows from Financing Activities:
  Additions to NationsBank loans                                   30,000             55,000
  Capital contributions                                                --                 10
  Distributions to owners                                              --            (44,128)
  Payment of floating rate notes                                       --            (10,000)
                                                                 --------           --------
       Net cash provided by financing activities                   30,000                882
                                                                 --------           --------

Increase (decrease) in cash and cash equivalents                    8,068             (1,252)
Cash and cash equivalents at beginning of period                   27,517             28,765
                                                                 --------           --------
Cash and cash equivalents at end of period                       $ 35,585           $ 27,513
                                                                 ========           ========

</TABLE>

                     SEE NOTES TO THE FINANCIAL STATEMENTS

                                       3
<PAGE>   6
                                   RCPI TRUST
                          NOTES TO FINANCIAL STATEMENTS
                                   (UNAUDITED)


1.   FINANCIAL STATEMENTS

     The balance sheet as of September 30, 1998, the statements of operations
     for the quarters ended and the nine months ended September 30, 1998 and
     1997 and the statements of cash flows for the nine months ended September
     30, 1998 and 1997 are unaudited, but in the opinion of the Company's
     management reflect all adjustments, consisting only of normal recurring
     adjustments, which are necessary to present fairly the financial condition
     and results of operations at those dates and for those periods. The results
     of operations for the interim periods are not necessarily indicative of
     results for a full year. It is suggested that these financial statements be
     read in conjunction with the audited financial statements and notes thereto
     included in the Company's latest Form 10-K for the year ended December 31,
     1997.


2.   DEBT

     NationsBank Credit Facility

     The Company entered into a Credit Agreement (the "NationsBank Credit
     Agreement") dated as of May 16, 1997, with NationsBank of Texas, N.A.
     ("NationsBank"), pursuant to which NationsBank agreed to make term loans
     (the "NationsBank Loans") to the Company in an aggregate principal amount
     of up to $100 million. As of December 31, 1997, the Company had a term loan
     outstanding in the principal amount of $55 million. On January 16, 1998,
     the Company entered into a second NationsBank loan in the principal amount
     of $20 million. On June 29, 1998, the Company entered into a third
     NationsBank loan in the principal amount of $10 million. As of September
     30, 1998 the total loans due to NationsBank were $85 million.

3.   SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES

     Prior Year Reclassifications

     Certain prior year balances have been reclassified to conform with the
     current year financial statement presentation.

                                       4
<PAGE>   7
                                   RCPI TRUST
                 ITEM 2. MANAGEMENT'S DISCUSSION AND ANALYSIS OF
                  FINANCIAL CONDITION AND RESULTS OF OPERATIONS


     LIQUIDITY AND CAPITAL RESOURCES - RCPI TRUST

     Land and Building

     At September 30, 1998, the Property, exclusive of 1.5 million square feet
     owned directly by the National Broadcasting Company, Inc. and NBC Trust No.
     1996A, was approximately 89.6% occupied. Occupancy rates for the Property
     at various dates are presented in the following table:

<TABLE>
<CAPTION>
<S>                                  <C>           <C>                      <C>
         June 30, 1998               88.1%         September 30, 1997       86.3%
         March 31, 1998              88.1%         June 30, 1997            86.4%
         December 31, 1997           86.7%         March 31, 1997           83.3%
</TABLE>

     The following table shows selected lease expirations and vacancy of the
     Property as of September 30, 1998. Area, as presented below and discussed
     above, is measured based on standards promulgated by the New York Real
     Estate Board in 1987. Lease turnover could offer an opportunity to increase
     the revenue of the Property or might have a negative impact on the
     Property's revenue. Actual renewal and rental income will be affected
     significantly by market conditions at the time and by the terms at which
     the Company can then lease space.

<TABLE>
<CAPTION>
                                   Square Feet               Percent
               Year                  Expiring                Expiring
               ----                  --------                --------
<S>            <C>                 <C>                      <C>
               Vacant                611,864                  10.4%
               1998                  175,022                   3.0%
               1999                  207,662                   3.5%
               2000                  467,798                   7.9%
               2001                  132,037                   2.2%
               2002                  218,162                   3.7%
               Thereafter          4,087,152                  69.3%
                                   ---------                  -----
               Total               5,899,697                 100.0%
                                   =========                 ======
</TABLE>

     Debt

     The Zero Coupon Debentures due December 31, 2000 accrete to a face value of
     approximately $586.2 million at an effective annual interest rate of
     12.10%. At September 30, 1998 and December 31, 1997, the carrying value of
     the Zero Coupon Debentures, net of unamortized discount, was approximately
     $447.1 million and $408.5 million, respectively.

     On July 17, 1996, outstanding principal on the Floating Rate Notes in the
     amount of $106.3 million plus accrued interest of $1.2 million was prepaid.
     On May 16, 1997, the remaining principal balance of $10 million was repaid.

                                       5
<PAGE>   8
                                   RCPI TRUST
                 ITEM 2. MANAGEMENT'S DISCUSSION AND ANALYSIS OF
                  FINANCIAL CONDITION AND RESULTS OF OPERATIONS


     The 14% Debentures have a principal balance of $75 million and mature on
     December 31, 2007. At the time the Property was acquired by the Company,
     the carrying value of the 14% Debentures was adjusted to reflect their
     estimated fair value at that date, resulting in a premium. The effective
     interest rate, which is net of the amortization of this premium, is
     approximately 9.03%. Interest payments are made semi-annually on July 31
     and January 31. As of September 30, 1998 and December 31, 1997, the
     carrying value of the 14% Debentures was approximately $98.5 million and
     $99.7 million, respectively.

     As of September 30, 1998, the NationsBank credit facility has an aggregate
     principal balance of $85 million and matures on May 16, 2000. The Company
     may elect interest periods based on one, two, three or six month LIBOR
     rates. Interest accrues at LIBOR plus 1.75% and is payable monthly in
     arrears.

     Cash Flow

     During the nine months ended September 30, 1998, the Company received cash
     flows of approximately $24 million from operations of the Property. The
     Company used part of this cash flow from operations and an additional draw
     on the NationsBank credit facility of $30 million to fund building
     improvements, tenant improvements, leasing commissions and other deferred
     costs totaling approximately $46 million.

     The Company believes that its current cash balance and future cash flows
     from operations, together with its expected borrowings in an amount
     currently believed not to exceed the current NationsBank Facility balance
     as of September 30, 1998 of $85 million, will be sufficient to fund its
     requirements for the foreseeable future.

     Inflation

     Inflation and changing prices during the current period did not
     significantly affect the markets in which the Company conducts its
     business. In view of the moderate rate of inflation, its impact on the
     Company's business has not been significant.

     RESULTS OF OPERATIONS - RCPI TRUST

     Base rent for the quarter and the nine months ended September 30, 1998
     increased approximately $5.9 million and $17.3 million, respectively, from
     the quarter and the nine months ended September 30, 1997, due mainly to
     higher rental rates on new leases than existed in the prior year.
     Additionally, the occupancy level increased to 89.6% as of September 30,
     1998, as compared to 86.3% as of September 30, 1997.

     Interest expense has increased by approximately $1.7 million and $5.7
     million for the quarter and the nine months ended September 30, 1998,
     respectively, as compared to the quarter and the nine months ended
     September 30, 1997, primarily due to the increase in the outstanding debt
     balance. Total outstanding debt as of September 30, 1997 was approximately
     $551 million, as compared to $631 million as of September 30, 1998. The
     increase is due primarily to accretion of the Zero Coupon Debentures and
     additional draws under the NationsBank credit facility which has increased
     by $30 million since September 30, 1997.

                                       6
<PAGE>   9
                                   RCPI TRUST
                 ITEM 2. MANAGEMENT'S DISCUSSION AND ANALYSIS OF
                  FINANCIAL CONDITION AND RESULTS OF OPERATIONS

     The increase in payroll and benefits of approximately $732,000 and $1.8
     million during the quarter and the nine months ended September 30, 1998,
     respectively, as compared to the quarter and the nine months ended
     September 30, 1997, is a result of additional salaries related to retail
     leasing and redevelopment.

     The increase in repairs, maintenance and supplies of approximately $475,000
     and $2.0 million during the quarter and the nine months ended September 30,
     1998, respectively, as compared to the quarter and the nine months ended
     September 30, 1997, is primarily due to additional asbestos costs incurred
     related to office and retail tenant construction and base building upgrades
     and construction which increased in 1998.

     Utilities expense for the quarter and the nine months ended September 30,
     1998 decreased by approximately $542,000 and $2.3 million, respectively, as
     compared to the quarter and nine months ended September 30, 1997, primarily
     due to a warm winter in the New York area, as well as operating
     efficiencies achieved through preventive maintenance.

     The decrease in professional fees in 1998 is due primarily to legal and
     settlement costs incurred during the first quarter of 1997 associated with
     the Bear Stearns & Co., Inc. and Donaldson, Lufkin & Jenrette Securities
     Corporation lawsuit, totaling approximately $2.6 million.

     General and administrative costs have increased during the quarter and the
     nine months ended September 30, 1998, as compared to the quarter and the
     nine months ended September 30, 1997, by approximately $118,000 and $1.2
     million, respectively. The increase is primarily due to a retroactive
     payment of city franchise and license fees based on a renegotiated contract
     and an increase in administrative costs related to the retail leasing and
     redevelopment.

     The increase in depreciation and amortization expense of approximately $1.1
     million and $3.2 million for the quarter and the nine months ended
     September 30, 1998, respectively, as compared to the quarter and the nine
     months ended September 30, 1997, was primarily due to additional capital
     projects at the property being placed into service since September 30, 1997
     and due to additional tenant improvements and leasing commissions expended
     as a result of increased office and retail leasing activity.

                                       7
<PAGE>   10
                                   RCPI TRUST
                           PART II - OTHER INFORMATION


     Item 1.Legal Proceedings

     Except as disclosed below, there has been no material change to the status
     of existing litigation as reported in the Company's Form 10-K filed as of
     December 31, 1997 and Form 10-Q filed as of June 30, 1998.

                                       8
<PAGE>   11
ITEM 6.  (a) EXHIBITS

<TABLE>
<CAPTION>
<S>            <C>
(3.1)          Certificate of Trust of RCPI Trust, dated March 22, 1996 is
               incorporated by reference to Exhibit 3.1 to the Company's
               Quarterly Report on Form 10-Q for the fiscal quarter ended June
               30, 1996.

(4.1)          Amended and Restated Debenture Purchase Agreement dated as of
               July 17, 1996 between the Company and WHRC Real Estate Limited
               Partnership is incorporated by reference to exhibit 4.1 to the
               Company's Annual Report on Form 10-K for the year ended December
               31, 1996 (the "1996 10-K").

(4.2)          Indenture dated as of September 15, 1985 between the Predecessor
               and Manufacturers Hanover Trust Company, as Trustee, including
               the forms of Current Coupon Convertible Debenture, Zero Coupon
               Convertible Debenture and Floating Rate Note, is incorporated by
               reference to Exhibit 4 to the Predecessor's Quarterly Report on
               Form 10-Q for the period ended September 30, 1985.

(4.3)          First Supplemental Indenture dated as of December 15, 1985
               between the Predecessor and the Trustee, is incorporated by
               reference to the Predecessor's Annual Report on Form 10-K for the
               year ended December 31, 1985.

(4.4)          Second Supplemental Indenture dated as of July 10, 1996 between
               the Company and the United States Trust Company of New York, as
               Trustee is incorporated by reference to exhibit 4.4 to the 1996
               10-K.

(4.5)          Instrument of Resignation, Appointment and Acceptance dated as of
               December 1, 1993 among the Predecessor, Chemical Bank, successor
               by merger to Manufacturers Hanover Trust Company, and United
               States Trust Company of New York is incorporated by reference to
               Exhibit 4.21 to the Predecessor's Annual Report on Form 10-K for
               the year ended December 31, 1993.

(10.1)         Amended and Restated Loan Agreement dated as of July 17, 1996
               among the Company, the lenders parties thereto and GSMC, as
               agent, is incorporated by reference to Exhibit 10.1 to the 1996
               10-K.

(10.2)         Guarantee dated July 17, 1996 by Whitehall Street Real Estate
               Limited Partnership V, Exor Group S.A., Tishman Speyer Crown
               Equities, David Rockefeller, Troutlet Investments Corporation,
               Gribble Investments (Tortola) BVI, Inc. and Weevil Investments
               (Tortola) BVI, Inc., as guarantors in favor of GSMC, as agent and
               lender, is incorporated by reference to Exhibit 10.2 to the 1996
               10-K.

(10.3)         Agreement and Plan of Merger dated as of November 7, 1995 among
               the Predecessor, RCPI Holdings Inc., RCPI Merger Inc., Whitehall
               Street Real Estate Limited Partnership V, Rockprop, L.L.C., David
               Rockefeller, Exor Group S.A. and Troutlet Investments Corporation
               is incorporated by reference to Exhibit 10.28 to the
               Predecessor's Current Report on Form 8-K dated November 13, 1995.

(10.4)         Amendment No. 1 dated as of February 12, 1996 to the Agreement
               and Plan of Merger dated as of November 7, 1995 among the
               Predecessor, RCPI Holdings Inc., RCPI Merger Inc.,
</TABLE>

                                       9
<PAGE>   12
ITEM 6. (a) EXHIBITS (Cont'd)

<TABLE>
<CAPTION>
<S>            <C>
               Whitehall Street Real Estate Limited Partnership V, Rockprop,
               L.L.C., David Rockefeller, Exor Group S.A. and Troutlet
               Investments Corporation is incorporated by reference to Exhibit
               10.31 to the Predecessor's Current Report on Form 8-K dated
               February 22, 1996.

(10.5)         Amendment No. 2 to the Agreement and Plan of Merger, dated as of
               April 25, 1996 is incorporated herein by reference to the
               Predecessor's Current Report on Form 8-K, filed on April 25,
               1996.

(10.6)         Amendment No. 3 to the Agreement and Plan of Merger, dated as of
               May 29, 1996 is incorporated herein by reference to the
               Predecessor's Current Report on Form 8-K, filed on May 29, 1996.

(10.7)         Amendment No. 4 to the Agreement and Plan of Merger, dated as of
               June 30, 1996 is incorporated herein by reference to the
               Predecessor's Current Report on Form 8-K, filed on July 1, 1996.

(10.8)         Credit Agreement, dated as of May 16, 1997, between the Company
               and NationsBank of Texas, N.A. is incorporated by reference to
               Exhibit 4.6 to the Company's Quarterly Report on Form 10-Q for
               the period ended June 30, 1997.

(10.9)         Intercreditor and Subordination Agreement, dated as of May 16,
               1997, between the Company and Whitehall is incorporated by
               reference to Exhibit 4.7 to the Company's Quarterly Report on
               Form 10-Q for the period ended September 30, 1997.

(10.10)        Limited Resource Agreement, dated as of May 16, 1997, is
               incorporated by reference to Exhibit 4.8 to the Company's
               Quarterly Report on Form 10-Q for the period ended June 30, 1997.

(27.1)         Company's Financial Data Schedule.
</TABLE>


      (b) REPORTS ON FORM 8-K

         No Current Reports on Form 8-K have been filed during the last fiscal
quarter.

                                       10
<PAGE>   13
                                   SIGNATURES


     Pursuant to the requirements of the Securities Exchange Act of 1934, the
     registrant has duly caused this report to be signed on its behalf by the
     undersigned thereunto duly authorized.

                                                 RCPI TRUST




     Date:   November 13, 1998                   By:/s/ David Augarten
                                                    ---------------------------
                                                    David Augarten
                                                    Vice President
                                                    (Principal Financial
                                                     Officer)

                                       11