Safeway Stores Inc. stock soared yesterday on rumors that the Herbert H. Haft family of Washington was about to make its long-awaited bid to buy the world's largest supermarket chain.

Fueling the speculation was a rumor that the Wall Street investment firm Drexel Burnham Lambert was arranging a part-stock, part-cash bid for Safeway on the Hafts' behalf, with a total per-share price of approximately $60. If so, that would make the entire offer worth $3.7 billion.

Meanwhile, some analysts reported speculation that Safeway was about to enter into a friendly merger with another company to ward off a takeover by the Haft family, which founded the Dart Drug store chain, Trak Auto Corp. and Crown Books Corp.

Overall, the rumors pushed the stock up $3.88 a share from Tuesday, to close at $51.50, with more than 2 million shares traded.

A Haft spokesman declined to comment on the speculation. Safeway Chief Financial Officer Harry Sunderland also declined comment.

But stock traders described yesterday's jump in price of Safeway stock as very dramatic. "For the past week, the stock has been sitting around the same price despite a lot of volume traded," noted one trader, who declined to be named. But yesterday, he said, "once the stock got past 48, it just kept going and going and going," with unusually large trades taking place on the Pacific Stock Exchange after the New York Stock exchange closed.

Safeway was the fifth most actively traded stock on the New York Stock Exchange, posting the third-largest dollar gain of all stocks traded yesterday.

On June 12, the Hafts notified the Securities and Exchange Commission that they had acquired 5.9 percent of Safeway stock "with a view to the possibility of acquiring all of or a majority interest" in the supermarket chain.

Safeway immediately vowed to fight any bid from the Hafts, saying it intended to remain an independent company. Last week, the chain sued the family, seeking to bar the Hafts from buying more Safeway shares on grounds that the family was illegally buying the stock and spreading rumors about a takeover for personal gain.

The Hafts called the suit frivolous and unfounded.

Although many Wall Street traders have said they doubted that the Haft family has enough money to buy Safeway, the appearance of Drexel Burnham's name has diminished those doubts.

Drexel is known for its ability to quickly raise billions of dollars for hostile takeovers through the sale of risky, high-yielding securities known as junk bonds. As a result, with Drexel's backing, the Hafts would not need to have the cash resources on their own.