Reliance Financial Services Corp., a subsidiary of the Reliance Group, has become the single largest shareholder in San Juan Racing Association Inc., which owns radio stations WUST-AF and WJBM-FM in Washington. Despite its large holdings, Reliance has no plans to acquire the company, according to San Juan's chairman.

According to a report filed with the Securities and Exchange Commission, Reliance has acquired 481,020 shares of common stock, or 12.2 percent, of San Juan Racing, which also owns a racetrack in Puerto Rico and eight other radio stations. Reliance is an insurance holding company.

San Juan, which has been looking for a buyer, is negotiating with Gulf Broadcast Group, an affiliate of Gulf United Corp., which is also in the insurance business.

"Conversations are proceeding, and intensive work is being done." said J. J. Glickstein, chairman and president of San Juan. Glickstein and Washington attorney Raymond R. Dickey, who is on the board, both indicated that a contract might be concluded within a month.

Dickey said the contract under discussion is a "contract to enter into a contract" that would call for further negotiations.

Glickstein said that Reliance "told us that additional purchases of stock, like their initial purchase of stock, were for investment only." Before its purchase of additional shares in May, Reliance held about 8 percent of San Juan's stock.

Before it began negotiating with Gulf Broadcasting, San Juan had been talking with Shamrock Broadcasting, a company owned by the family of Roy E. Disney, brother of the late Walt Disney. Thoes talks ended in March.