Beleaguered Internet search company Yahoo is in talks with Time Warner to acquire AOL, according to a report Thursday.

The Bloomberg report comes days after Yahoo announced that Chief Executive Jerry Yang is stepping down and Microsoft Chief Executive Steve Ballmer repeated that he would be open to a deal for Yahoo’s search business, but not an outright acquisition.

On the report, beaten-down shares of Yahoo tacked on $.21, or 2.3 percent, to $9.35, while Time Warner lost $.39, or 4.7 percent, to $7.76.

Bloomberg, quoting unidentified sources, said executives of Yahoo and Time Warner have been meeting over several weeks, but have not agreed on terms.

Mr. Ballmer, while keeping open the possibility of a deal for Yahoo’s search, said Wednesday that Microsoft has no interest in acquiring Yahoo. On February 1, Microsoft offered $31 per share, or $44.6 billion, to acquire Yahoo. In June, however, the Redmond, Washington, software company abandoned the effort.

Bloomberg quoted Jeff Lindsay, an analyst at Sanford C. Bernstein, as saying that Yahoo and AOL would have to cut up to 3,000 jobs to make the “high-risk” deal worthwhile.

AOL, long the leading U.S. Internet service provider, has transitioned into an online advertising platform that also delivers content and Web services like e-mail.