<PAGE>   1
                                  UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                              Washington, DC 20549

                                    FORM 10-Q

[X]      Quarterly report pursuant to Section 13 or 15(d) of the
         Securities and Exchange Act of 1934

For the quarterly period ended          November 7, 1997

                                       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   1-7623

                           GENOVESE DRUG STORES, INC.
             (Exact name of registrant as specified in its charter)

           DELAWARE                                          11-1556812
(State of other jurisdiction of                            (I.R.S. Employer
 incorporation or organization)                           Identification No.)

                    80 Marcus Drive, Melville, New York 11747
                    (Address of principal executive offices)
                                   (Zip Code)

                                 (516) 420-1900
              (Registrant's telephone number, including area code)

                                      NONE
        (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
    ---     ---

Indicate the number of shares outstanding of each of the issuer's classes of
common stock, as of the close of the period covered by this report.
<TABLE>
<CAPTION>
              CLASS                              OUTSTANDING AT NOVEMBER 7, 1997
              -----                              -------------------------------
<S>                                              <C>
COMMON STOCK:
Class A, par value $1.00 per share                    6,447,983
Class B, par value $1.00 per share                    5,974,368
</TABLE>
<PAGE>   2
                           GENOVESE DRUG STORES, INC.

                                      INDEX

<TABLE>
<CAPTION>
                                                                                PAGE
                                                                                ----

<S>                                                                           <C>
PART I.           FINANCIAL INFORMATION

                  Condensed Balance Sheets - November 7, 1997
                  (Unaudited) and January 31, 1997                                2

                  Condensed Statements of Income - Twelve  and
                  Forty Weeks Ended November 7, 1997 and
                  November 8, 1996 (Unaudited)                                    3

                  Condensed Statements of Cash Flows -
                  Forty Weeks Ended November 7, 1997 and
                  November 8, 1996 (Unaudited)                                    4

                  Notes to Unaudited Condensed Financial
                  Statements                                                      5

                  Management's Discussion and Analysis of
                  Financial Condition and Results of Operations               6 - 8


PART II.          OTHER INFORMATION AND SIGNATURES                                8


EXHIBIT 11 -         Statement Re:  Computation of Net Income
                     Per Common Share                                             9
</TABLE>
<PAGE>   3
                           GENOVESE DRUG STORES, INC.
                            CONDENSED BALANCE SHEETS
                             (Dollars in Thousands)

<TABLE>
<CAPTION>
                                                                                  November 7,       January 31,
                                                                                     1997              1997
                                                                                  -----------       -----------
                                                                                  (Unaudited)         (Note 1)
<S>                                                                               <C>               <C>

                                     ASSETS

Current Assets:
    Cash                                                                             $  2,128         $  2,368
    Receivables                                                                        19,059           21,179
    Merchandise inventory                                                             128,323          113,182
    Prepaid expenses and other                                                          1,869            4,527
                                                                                     --------         --------

         Total Current Assets                                                         151,379          141,256
                                                                                     --------         --------

Property and Equipment, net                                                            83,520           79,435
                                                                                     --------         --------

Other Assets                                                                           12,901            9,372
                                                                                     --------         --------

         Total Assets                                                                $247,800         $230,063
                                                                                     ========         ========


                      LIABILITIES AND STOCKHOLDERS' EQUITY

Current Liabilities:
    Accounts payable, accrued expenses
      and other                                                                      $ 84,452         $ 87,958
    Current portion of long-term debt                                                     871              871
                                                                                     --------         --------

         Total Current Liabilities                                                     85,323           88,829
                                                                                     --------         --------

Long-Term Liabilities                                                                  77,468           55,073
                                                                                     --------         --------

Deferred Income Taxes Payable                                                           5,881            8,481
                                                                                     --------         --------

Stockholders' Equity                                                                   79,128           77,680
                                                                                     --------         --------

         Total Liabilities and
           Stockholders' Equity                                                      $247,800         $230,063
                                                                                     ========         ========
</TABLE>


      See accompanying notes to unaudited condensed financial statements.


                                       -2-
<PAGE>   4
                           GENOVESE DRUG STORES, INC.
                         CONDENSED STATEMENTS OF INCOME
                 (Dollars in Thousand Except Per Share Amounts)
                                   (Unaudited)
<TABLE>
<CAPTION>
                                                       Twelve Weeks Ended                      Forty Weeks Ended
                                                 -------------------------------         -------------------------------
                                                 November 7,         November 8,         November 7,         November 8,
                                                     1997                1996               1997                1996
                                                 -----------         -----------         -----------         -----------
<S>                                              <C>                 <C>                 <C>                 <C>
Sales                                            $   175,246         $   159,108         $   575,219         $   515,723
                                                 -----------         -----------         -----------         -----------

Cost and Expenses:
    Cost of merchandise sold                         126,185             111,450             415,195             365,015
    Selling, general and
      administrative expenses                         47,191              42,541             150,817             137,841
                                                 -----------         -----------         -----------         -----------
                                                     173,376             153,991             566,012             502,856
                                                 -----------         -----------         -----------         -----------

Operating Profit                                       1,870               5,117               9,207              12,867

Interest Expense                                         952                 918               2,761               3,131
                                                 -----------         -----------         -----------         -----------

Income Before Income Taxes                               918               4,199               6,446               9,736
Income Taxes                                             401               1,848               2,817               4,284
                                                 -----------         -----------         -----------         -----------

Net Income                                       $       517         $     2,351         $     3,629         $     5,452
                                                 ===========         ===========         ===========         ===========

Net Income Per Common Share (a)                  $       .04         $       .19         $       .29         $       .45
                                                 ===========         ===========         ===========         ===========

Average Number of Common Shares
  Outstanding (a)                                 12,419,000          12,233,000          12,381,000          12,221,000
                                                 ===========         ===========         ===========         ===========

Cash Dividends Paid Per Common Share (a)         $       .07         $       .05         $       .20         $       .16
                                                 ===========         ===========         ===========         ===========
</TABLE>



(a)      Adjusted where appropriate, to retroactively reflect the effect of a 10
         percent stock dividend distributed on January 14, 1997.


See accompanying notes to unaudited condensed financial statements.


                                       -3-
<PAGE>   5
                           GENOVESE DRUG STORES, INC.
                       CONDENSED STATEMENTS OF CASH FLOWS
                             (Dollars in Thousands)
                                   (Unaudited)

<TABLE>
<CAPTION>
                                                                 Forty Weeks Ended
                                                            ------------------------------
                                                            November 7,        November 8,
                                                               1997               1996
                                                            -----------        -----------
<S>                                                         <C>                <C>
Cash flows from operating activities:
    Net income                                               $  3,629          $  5,452
    Adjustment to reconcile net income to
      net cash used for operating activities:
          Depreciation and amortization                        10,221             8,739
          Provision for LIFO inventory valuation                1,600             1,300
          Provision for deferred taxes                         (2,600)               --
          Provision for other non cash items                       39               (45)
          Changes in certain assets and liabilities:
            Receivables                                         2,120            (4,126)
            Merchandise inventory                             (17,148)          (10,663)
            Prepaid expenses                                    2,497             3,705
            Other assets                                       (4,472)           (3,484)
            Supplier advances                                   6,006                --
            Accounts payable, accrued expenses
              and other                                        (4,373)            2,614
                                                             --------          --------

Net cash provided by operating activities                      (2,481)            3,492
                                                             --------          --------

Cash flows from investing activities:
    Purchase of property and equipment, net                   (16,741)          (13,853)
    Proceeds from the sale of the Living
      Color Photo Processing Lab                                3,952                --
                                                             --------          --------

Net cash used for investing activities                        (12,789)          (13,853)
                                                             --------          --------

Cash flows from financing activities:
    Net increase in bank borrowings                            18,000            12,450
    Repayments of long-term liabilities                          (744)             (646)
    Payment of cash dividends                                  (2,478)           (2,000)
    Issuance of common stock under the Employee
      Stock Option and Rights Appreciation Plan                 1,352               340
    Treasury stock purchased                                   (1,100)             (234)
                                                             --------          --------

Net cash provided by financing activities                      15,030             9,910
                                                             --------          --------

Net decrease in cash                                             (240)             (451)
Cash at beginning of period                                     2,368             2,251
                                                             --------          --------

Cash at end of period                                        $  2,128          $  1,800
                                                             ========          ========

Supplemental disclosure:
    Interest paid                                            $  2,786          $  2,914
                                                             ========          ========
    Income taxes paid                                        $  7,118          $  3,486
                                                             ========          ========
</TABLE>


    See the accompanying notes to unaudited condensed financial statements.

                                       -4-
<PAGE>   6
                           GENOVESE DRUG STORES, INC.
                NOTES TO UNAUDITED CONDENSED FINANCIAL STATEMENTS


1.       The condensed balance sheet as of November 7, 1997, the condensed
         statements of income for the twelve and forty week periods ended
         November 7, 1997 and November 8, 1996 and the condensed statements of
         cash flows for the forty week periods ended November 7, 1997 and
         November 8, 1996 have been prepared in accordance with generally
         accepted accounting principles for interim financial information and
         with the instructions for Form 10-Q and Article 10 of Regulations S-X
         by the Company, without audit. The balance sheet as of January 31, 1997
         was derived from the audited balance sheet included in the Company's
         Annual Report on Form 10-K. In the opinion of management, all
         adjustments (which include only normal recurring adjustments) necessary
         to present fairly the financial condition, results of operations and
         cash flows at November 7, 1997 and for the periods presented have been
         made.

         Certain information and footnote disclosures normally included in
         financial statements prepared in accordance with generally accepted
         accounting principles have been condensed or omitted. These condensed
         financial statements should be read in conjunction with the financial
         statements and notes thereto included in the Company's Annual Report on
         Form 10-K for the year ended January 31, 1997.

2.       The results of operations for the twelve and forty weeks ended November
         7, 1997 and November 8, 1996 are not necessarily indicative of the
         results to be expected for the full year.

3.       Merchandise inventory is valued at the lower of cost or market, cost
         being determined by the last in first out (LIFO) method. LIFO inventory
         costs are determined at the end of each fiscal year when inflation
         rates are finalized. Therefore, LIFO inventory costs and cost of
         merchandise sold for interim periods are estimated and adjusted based
         on periodic physical inventories. At November 7, 1997 and January 31,
         1997, inventories would have been greater by $20,300,000 and
         $18,700,000, respectively, if they had been valued at replacement
         costs.

4.       During the forty weeks ended November 7, 1997, the Company sold the
         assets of its Living Color photo processing plant. Simultaneously with
         the sale of the processing plant, the Company entered into an agreement
         whereby the Company will outsource all of its out of store
         photofinishing.

5.       On December 9, 1997 the Company's Board of Directors declared a 10
         percent stock dividend payable on January 14, 1998 to holders of record
         as of December 26, 1997.

         The Board of Directors also declared a cash dividend of $.07 per common
         share payable on January 14, 1998 to holders of record as of December
         26, 1997. The cash dividend will be payable on the shares represented
         by the stock dividend.


                                       -5-
<PAGE>   7
                     MANAGEMENT'S DISCUSSION AND ANALYSIS OF
                  FINANCIAL CONDITION AND RESULTS OF OPERATIONS



     FOR THE TWELVE AND FORTY WEEKS ENDED NOVEMBER 7, 1997


     Sales increased by 10.1% for the third quarter and 11.5% for the year to
     date. On a comparable store basis (stores which were open during all of
     fiscal 1997 and 1998 to date), sales increased by 5.6% for the quarter and
     7.1% for the year to date. The sales contribution of the 23 stores opened
     during fiscal 1996, 1997 and 1998 to date in addition to the maturation of
     existing stores were the primary components of the sales increases. Sales
     have also been effected by an undetermined amount of inflationary price
     increases which have been passed onto customers.

     Cost of merchandise sold, expressed as a percentage of sales, increased to
     72.0% for the third quarter versus 70.0% last year. The results for the
     first half followed the same trend with the cost of merchandise sold at
     72.2% this year versus 70.8% last year. The primary factors resulting in
     the decrease in gross profit margins are the continued reduction of
     reimbursement rates from third party prescription plans, the increase in
     pharmacy sales as a percentage of total sales and the increase in third
     party plan sales as a percentage of pharmacy sales. For the year to date,
     prescription sales represented 41.0% of total sales versus 38.8% in fiscal
     1997. Pharmacy sales to individuals covered by third party prescription
     plans increased to 79.6% this year from 75.2% in the same period last year.
     Management anticipates that pharmacy margins will continue to decline
     throughout fiscal 1998 and during fiscal 1999 due to continued pressure on
     third party reimbursement rates and the increasing percentage of customers
     covered by third party prescription plans.

     Selling, general and administrative expenses increased to 26.9% of sales
     from 26.7% for the third quarter, and decreased to 26.2% from 26.7% for the
     year to date. The increase in selling, general and administrative expenses
     during the quarter ended November 7, 1997 reversed the trend of decreasing
     selling, general and administrative expenses as a percentage of sales
     activities during the previous four quarters. This increase was primarily
     the result of costs associated with the implementation of a new pharmacy
     computer system combined with lower than expected sales growth partially
     due to the loss of sales from a major third party prescription plan, which
     the Company terminated due to low reimbursement rates.

     Interest expense was $952,000 for the third quarter versus $918,000 for the
     same period last year and $2,761,000 versus $3,131,000 for the year to
     date. The increase in interest expense during the third quarter was a
     result of higher borrowing levels outstanding during the quarter.

     Net income for the third quarter decreased to $517,000, or $.04 per share,
     from $2,351,000, or $.19 per share, last year. Net income for the year to
     date was $3,629,000, or $.29 per share, versus $5,452,000, or $.45 per
     share, last year.

                                       -6-
<PAGE>   8
     FINANCIAL CONDITION

The Company's operating, investing and financing activities for the forty weeks
ended November 7, 1997 used net cash of $240,000 as follows:

-    Operating activities used $2,481,000 primarily due to increases in
     merchandise inventory and other assets and a decrease in accounts payable,
     accrued expenses and other, which were partially offset by decreases in
     receivables, prepaid expenses and the receipt of supplier advances.

-    Investing activities used $12,789,000 due to the purchase of property and
     equipment of $16,741,000, which was partially offset by proceeds from the
     sale of the Living Color photo processing plant.

-    Financing activities provided $15,030,000 primarily from additional bank
     borrowing partially offset by the repayment of long-term debt and the
     payment of cash dividends.

Working capital at November 7, 1997 was $66.1 million. The working capital ratio
was 1.8 to 1.0 at November 7, 1997 versus 1.6 to 1.0 at January 31, 1997.

The Company maintains a revolving credit facility with three banks under which
the banks are committed to lend up to $90 million to the Company. As of November
7, 1997, the Company had borrowings of $62 million under this agreement. As of
November 7, 1997, the Company was in compliance with all loan covenants. Because
the payment of the recently declared cash dividend on January 14, 1998 could
have caused the Company, based on its projected results for the fourth quarter
of fiscal 1998, to be in default of its loan covenant with respect to payment of
dividends, the Company requested and received a waiver of this covenant for the
fiscal year ending January 30, 1998.

The Company anticipates that its working capital needs for the remainder of
fiscal 1998 will be satisfied through operating results and, as necessary,
through borrowing under facilities available to the Company.

RECENT ACCOUNTING PRONOUNCEMENTS

In February 1997, the Financial Accounting Standards Board issued Statement of
Financial Accounting Standards No. 128 "Earnings Per Share" ("SFAS 128"). SFAS
128 establishes standards for computing and presenting earnings per share
("EPS"). SFAS 128 replaces the presentation of primary EPS with the presentation
of basic EPS and requires the presentation of basic EPS and diluted EPS on the
face of the income statement.

This statement will be effective for the Company's fiscal year ending January
30, 1998. Early application for the quarter ended November 7, 1997 is not
permitted.

If SFAS 128 had been adopted for the twelve and forty weeks ended November 7,
1997 and November 8, 1996, there would have been no difference in the reported
earnings per share.


                                       -7-
<PAGE>   9
This 10-Q contains "forward looking statements" based on the Company's current
plans and expectations, which involve risk and uncertainties. Actual results or
achievements may be materially different. The Company's plans and expectations
are based on assumptions involving judgements with respect to future economic,
competitive and market conditions and future business decisions, all of which
are difficult or impossible to predict accurately and many of which are beyond
the control of the Company. The Company's experience under third party
prescription reimbursement plans will be subject to industry trends in managed
care, and the nature, timing and frequency of amendments, modifications, or
expirations of such agreements. Therefore, there can be no assurance that the
forward looking statements will prove to be accurate. The Company undertakes no
obligation to revise its forward looking statements to reflect events or
circumstances after the date hereof.

                                     ******


PART II.          OTHER INFORMATION


Item 6.  Exhibits and Reports on Form 8-K

The following exhibit is included herein:

(11) Statement re:  computation of net income per common share.

There were no reports on Form 8-K filed during the twelve week period ended
November 7, 1997.




                                   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.


                                             GENOVESE DRUG STORES, INC.
                                                   (Registrant)




Date:    December 19, 1997                   By:  /s/    Jerome Stengel
      ----------------------                      -------------------------
                                                         Jerome Stengel
                                                  (Vice President & Treasurer)
                                                  (Principal Financial Officer)


                                       -8-