Raleigh Stores Corp. yesterday said it would complete its $85 million purchase of the 10-store Garfinckel's chain Wednesday, four days after the Aug. 15 deadline set by Allied Stories Corp., Garfinckel's present owner.

David Nellis, a Raleigh's spokesman, said the delay in closing the deal was due solely to paperwork, "crossing the t's and dotting the i's." He added, "There has never been any hangup on financing.

Initially, the 12-store Raleigh's chain had hoped to complete the purchase in mid-July. As a result, Garfinckel's top management, which had submitted a competing bid to buy the chain, left on July 15. Among those leaving was president Hanne Merriman, who submitted her resignation shortly after the Raleigh's sale was announced in early June. Six other top executives were dismissed by Raleigh's as of July 15.

Since then, the company's operations have remained in limbo, waiting for the completion of the deal. As each day passed without the closing, reports increased in the retailing community that Raleigh's and its chairman, Neal J. Fox, were having problems obtaining the financing needed to complete the deal. Among other things, retailing sources said Fox would have to sell Garfinckel's flagship store at 14th and F streets NW to help finance the acquisition. He could then lease the store back from the buyer to continue operations there.

Nellis, on behalf of Fox, yesterday emphatically denied those rumors and said that selling the F street building was never an issue in completing the deal. "I never intend to leave that site," Nellis quoted Fox as saying.

Garfinckel's was put up for sale in January after Allied Stores was sold to Campeau Corp. for $3.5 billion. To reduce the debt incurred from the sale, Campeau put 16 Allied divisions up for sale, including Garfinckel's and the Richmond-based Miller & Rhoads department store chain.

First Boston Corp., which is handling the sale for Allied, yesterday declined to comment on the closing of the Garfinckel's sale or its timing. Nellis, however, said "all substantial issues have been resolved."

When the acquisition is completed, Fox plans to run the chains as separate entities.