<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 EXCHANGE ACT OF 1934

For the quarterly period ended        November 8, 1996
                                -------------------------------

                                       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 or 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 8, 1996
----------------------------------               -------------------------------
<S>                                              <C>    
COMMON STOCK:                                    
Class A, par value $1.00 per share                  5,646,621   Class A shares
Class B, par value $1.00 per share                  5,514,189   Class B shares
</TABLE>
<PAGE>   2
                           GENOVESE DRUG STORES, INC.

                                      INDEX


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

           Condensed Balance Sheets - November 8, 1996
           (Unaudited) and February 2, 1996                           2

           Condensed Statements of Income - Twelve and
           Forty Weeks Ended November 8, 1996 and
           November 10, 1995 (Unaudited)                              3

           Condensed Statements of Cash Flows -
           Forty Weeks Ended November 8, 1996
           and November 10, 1995 (Unaudited)                          4

           Notes to Unaudited Condensed Financial Statements          5

           Management's Discussion and Analysis of Financial
           Condition and Results of Operations                      6-7

PART II.  OTHER INFORMATION AND SIGNATURES                          7-8

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


<TABLE>
<CAPTION>
                                       Assets
                                       ------



                                                          November 8,    February 2,
                                                             1996           1996
                                                           --------       --------
                                                          (Unaudited)     (Note 1)
<S>                                                        <C>            <C>     
Current Assets:
        Cash                                               $  1,800       $  2,251
        Receivables                                          18,662         14,396
        Merchandise inventory                               114,218        104,855
        Prepaid expenses and other                            1,384          5,089
                                                           --------       --------

     Total Current Assets                                   136,064        126,591
                                                           --------       --------

Property and Equipment, net                                  77,413         71,637
                                                           --------       --------

Other Assets                                                  8,635          5,813
                                                           --------       --------

                Total Assets                               $222,112       $204,041
                                                           ========       ========


                        Liabilities and Stockholders' Equity
                        ------------------------------------

Current Liabilities:
        Accounts payable, accrued expenses and other       $ 72,195       $ 69,651
        Current portion of long-term debt                       798            798
        Notes payable to banks                               25,200         15,250
                                                           --------       --------

                Total Current Liabilities                    98,193         85,699
                                                           --------       --------

Long-Term Liabilities                                        43,379         41,455
                                                           --------       --------

Deferred Income Taxes Payable                                 7,219          7,219
                                                           --------       --------

Stockholders' Equity:
     Common stock - $1.00 par value, 32,000,000
     shares authorized, 11,293,164 shares and
     11,236,673 shares issued at November 8, 1996
     and February 2, 1996, respectively                      11,293         11,237
     Capital in excess of par value                          56,560         56,182
     Retained earnings                                        7,008          3,556
                                                           --------       --------
                                                             74,861         70,975

   Less:  Common stock in treasury at cost -
     132,354 shares at November 8, 1996 and
     132,512 at February 2, 1996                              1,540          1,307
                                                           --------       --------

         Total Stockholders' Equity                          73,321         69,668
                                                           --------       --------

         Total Liabilities and Stockholders'
            Equity                                         $222,112       $204,041
                                                           ========       ========
</TABLE>


See accompanying notes to unaudited condensed financial statements.



                                       -2-
<PAGE>   4
                           GENOVESE DRUG STORES, INC.
                         CONDENSED STATEMENTS OF INCOME
                 (Dollars in Thousands Except Per Share Amounts)
                                   (Unaudited)


<TABLE>
<CAPTION>
                                              Twelve Weeks Ended                      Forty Weeks Ended          
                                       --------------------------------        --------------------------------
                                        November 8,        November 10,         November 8,        November 10,
                                           1996                1995                1996                1995
                                       ------------        ------------        ------------        ------------
<S>                                    <C>                 <C>                 <C>                 <C>         
Sales                                  $    159,108        $    137,719        $    515,723        $    454,968
                                       ------------        ------------        ------------        ------------

Cost and Expenses:
  Cost of merchandise sold                  111,450              95,744             365,015             322,352
  Selling, general and
         administrative expenses             42,541              37,932             137,841             122,728
                                       ------------        ------------        ------------        ------------
                                            153,991             133,676             502,856             445,080
                                       ------------        ------------        ------------        ------------

Operating Profit                              5,117               4,043              12,867               9,888
Gain on the sale of the
  nursing home division                          --                  --                  --               1,300
Interest Expense                               (918)               (793)             (3,131)             (2,818)
                                       ------------        ------------        ------------        ------------

Income Before Income Taxes                    4,199               3,250               9,736               8,370
Income Taxes                                  1,848               1,462               4,284               3,766
                                       ------------        ------------        ------------        ------------

Net Income                             $      2,351        $      1,788        $      5,452        $      4,604
                                       ============        ============        ============        ============

Net Income Per Common Share (a)        $        .21        $        .16        $        .49        $        .42
                                       ============        ============        ============        ============

Average Number of Common Shares
  Outstanding (a)                        11,121,000          11,085,000          11,110,000          11,084,000
                                       ============        ============        ============        ============

Cash Dividends Paid Per Common
  Share (a)                            $        .06        $        .05        $        .18        $        .16
                                       ============        ============        ============        ============
</TABLE>


(a)      Adjusted, where appropriate, to retroactively reflect the effect of a
         10 percent stock dividend distributed on January 4, 1996.

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 8,    November 10,
                                                         1996            1995
                                                      -----------    ------------
<S>                                                    <C>             <C>     
Cash Flows From Operating Activities:
  Net income                                           $  5,452        $  4,604
  Adjustments to reconcile net income to
    net cash provided by (used for) operating
     activities:
     Depreciation and amortization                        8,739           6,889
     Provision for LIFO inventory valuation               1,300           1,100
     Gain on the sale of the nursing home
      division                                               --          (1,300)
     Provision for other noncash expenses-net               (45)            214
     Changes in certain assets and liabilities:
         Receivables                                     (4,126)         (1,047)
         Merchandise inventory                          (10,663)        (15,496)
         Prepaid expenses and other                       3,705           1,801
         Other assets                                    (3,484)         (1,440)
         Accounts payable, accrued expenses
           and other                                      2,614             463
                                                       --------        --------
Net cash provided (used) by operating activities          3,492          (4,212)
                                                       --------        --------

Cash Flows From Investing Activities:
  Purchase of property and equipment, net               (13,853)        (11,782)
  Proceeds from the sale of the nursing
    home division                                            --           2,719
                                                       --------        --------

Net cash used for investing activities                  (13,853)         (9,063)
                                                       --------        --------

Cash Flows From Financing Activities:
  Net increase in debt                                   12,450          15,450
  Repayments of long term liabilities                      (646)           (834)
  Issuance of common stock under the Employee
    Stock Option and Appreciation Rights Plan               340              21
  Treasury stock purchased                                 (234)           (227)
  Payment of cash dividends                              (2,000)         (1,814)
                                                       --------        --------

Net cash provided by financing activities                 9,910          12,596
                                                       --------        --------

Net Decrease in Cash                                       (451)           (679)
Cash at Beginning of Period                               2,251           2,229
                                                       --------        --------

Cash at End of Period                                  $  1,800        $  1,550
                                                       ========        ========

Supplemental Disclosure:
  Interest paid                                        $  2,914        $  2,941
  Income taxes paid                                    $  3,486        $  5,826
</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 8, 1996, the condensed
         statements of income for the twelve and forty week periods ended
         November 8, 1996 and November 10, 1995 and the condensed statements of
         cash flows for the forty week periods ended November 8, 1996 and
         November 10, 1995 have been prepared in accordance with generally
         accepted accounting principles for interim financial information and
         with the instructions to Form 10-Q and Article 10 of Regulation S-X by
         the Company, without audit. The condensed balance sheet as of February
         2, 1996 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 8, 1996 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 February 2, 1996.

2.       The results of operations for the twelve and forty weeks ended November
         8, 1996 and November 10, 1995 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 8, 1996 and February 2,
         1996, inventories would have been greater by $20,250,000 and
         $18,950,000, respectively, if they had been valued at replacement
         costs.

4.       On December 10, 1996, the Company's Board of Directors declared a 10%
         stock dividend payable on January 14, 1997 to holders of record as of
         December 26, 1996.

         The Board of Directors also declared a cash dividend of $.06 per common
         share payable on January 14, 1997 to holders of record as of December
         27, 1996. 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 8, 1996

Sales increased by 15.5% for the third quarter and 13.4% for the year to date.
On a comparable store basis (stores open during all of fiscal 1996 and fiscal
1997 to date) sales increased 9.2% for the quarter and 8.1% for the year to
date. The sales contribution of the 16 stores opened during fiscal 1996 and
1997, the continued maturation of existing stores and the effects of the
Company's marketing programs were the primary causes for the increase in sales.

Cost of good sold, expressed as a percentage of sales, was 70.0% for the third
quarter versus 69.5% last year. On a year to date basis, cost of goods sold was
slightly improved 70.8% this year versus 70.9% last year. The primary factors
affecting cost of goods sold are product mix, efficiencies in merchandise
acquisition practices and a slowing of the decline in pharmacy margins related
to third party prescription plans.

Selling, general and administrative expenses, expressed as a percentage of
sales, declined to 26.7% from 27.5% for the quarter and to 26.7% from 27.0% for
the year to date. These decreases are the result of cost management programs
implemented by the Company.

Interest expense was $918,000 for the quarter versus $793,000 last year and
$3,131,000 for the year to date versus $2,818,000 for the corresponding period
last year. The increases in interest expenses are due to higher average
borrowings this year versus last year.

Net income per share increased 31.5% to $2,351,000 or $.21 per share from
$1,788,000 or $.16 last year. Net income for the year to date increased 18.4% to
$5,452,000 or $.49 per share versus $4,604,000 or $.42 last year. Last year's
net income for the forty weeks included a gain of $722,000 or $.07 per share
related to the sale of the Company's nursing home division.


FINANCIAL CONDITION

The Company's operating, investing and financing activities for the forty weeks
ended November 8, 1996 utilized net cash of $451,000 as follows:

         -     Operating activities provided $3,492,000. Operations provided
               $15,446,000 which was offset primarily by increases in
               merchandise inventory and receivables.

         -     Investing activities utilized $13,853,000 through the purchase of
               property and equipment.

         -     Financing activities provided $9,910,000 primarily from
               short-term borrowings partially offset by the repayment of
               long-term debt and the payment of cash dividends.


                                       -6-
<PAGE>   8
Working capital at November 8, 1996 was $37.9 million. The working capital ratio
was 1.4 to 1.0 at November 8, 1996 versus 1.5 to 1.0 at February 2, 1996.

The Company is currently renegotiating its credit facilities and has received a
letter of commitment from three banks to increase its credit facility from a $70
million facility to a $90 million credit facility.

The Company anticipates that its working capital needs for the remainder of
fiscal 1997 will be satisfied through operating results and, as necessary,
through borrowings under facilities available to the Company.


PART II.

Item 5.  Other Information

The Private Securities Litigation Reform Act of 1995 ("the Act") provides a safe
harbor for forward-looking statements made by or on behalf of the Company. All
statements, other than statements of historical facts, which address activities,
events or developments that the Company expects or anticipates will or may occur
in the future, including such things as future capital expenditures (including
the amount and nature thereof), expansion and other development trends of
industry segments in which the Company is active, business strategy, expansion
and growth of the Company's business and operations and other such matters are
forward looking statements. To take advantage of the safe harbor provided by the
Act, Genovese Drug Stores, Inc. is identifying certain factors that could cause
actual results to differ materially from those expressed in any forward-looking
statements, whether oral or written, made by or on behalf of the Company. Many
of these factors have previously been identified in filings or statements made
by or on behalf of the Company.

All phases of the Company's operations are subject to influences outside its
control. Any one, or a combination, of these factors could materially affect the
results of the Company's operations. These factors include: competitive
pressures, inflation, consumer debt levels, currency exchange fluctuations,
trade restrictions, changes in tariff and freight rates, political instability,
interest rate fluctuations and other capital market conditions. Forward-looking
statements made by or on behalf of the Company are based on a knowledge of its
business and the environment in which it operates, but because of the factors
listed above, actual results may differ from those in the forward-looking
statements. Consequently, all of the forward-looking statements made are
qualified by these cautionary statements and there can be no assurance that the
actual results or developments anticipated by the Company will be realized or,
even if substantially realized, that they will have the they will have the
expected consequences to or effect on the Company or its business or operations.


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 8, 1996.



                                       -7-
<PAGE>   9
                                   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, 1996           By: /s/ Jerome Stengel
      ---------------------             ---------------------------------
                                            Jerome Stengel
                                            (Vice President & Treasurer)
                                            (Principal Financial Officer)




                                       -8-