Retailing giant Sears Roebuck & Co. battled takeover rumors Friday in the first week of its 40-million-share stock buy-back effort, after posting its heaviest trading volume as its stock climbed to a 52-week high.

On Friday afternoon, Sears stock was selling for $45 per share on the New York Stock Exchange, off $1 from its previous close of $46 on Thursday's gains of $3. Sears' volume was approximately 2,205,000 shares.During Thursday's session, Sears stock rose on a volume of 8.2 million shares, the company's highest, and was the most active issue on the NYSE's Big Board. The previous daily record for Sears stock volume 5.2 million, posted Oct. 27.

The active trading was attributed to speculation that a takeover bid of $60 or $65 a share had been offered or was forthcoming. Revlon Corp. Chairman Ronald Perelman was reportedly putting together a $65-per-share bid, the Chicago Sun-Times reported.

There also were published reports that New York developer Donald Trump and JMB Realty Trust were buying Sears shares.

Sears declined comment on all speculation about potential suitors and did not respond to a request from NYSE officials that the retailer issue a public statement on what, if any, developments might explain the stock price rise.

"We don't comment on unusual trading activity or rumors," a Sears spokesman said.

A spokesman for Revlon also declined comment.

Analysts described any potential bid for Sears as a substantial move in light of current market values. Market observers said Sears' restructuring plan does not contain sufficient takeover barriers.

The runup in Sears' share price came three days after Edward A. Brennan, Sears chairman, announced the restructuring plan under which the firm would buy back as many as 40 million - about 10 percent - of its 380 million outstanding shares by mid-1989. Sears was believed to have begun buying shares Wednesday, but the spokesman declined comment on how many shares the merchandiser had repurchased.

A bid of $65 per share would total a staggering $25 billion.