(REUTERS) -- A consortium of software giant Microsoft Corp., private-equity group Silver Lake, and venture-capital firm Andreessen Horowitz are reworking their bid for a minority stake in Internet company Yahoo Inc., a source familiar with the matter said on Friday.

Silver Lake's consortium is working on a new offer for a stake of 10 to 15 percent in Yahoo after the company requested improved terms, the source said.

The new offer would be predicated on Yahoo finding a new, world-class CEO who the consortium would support, the source added. Yahoo's board fired CEO Carol Bartz in September and has yet to hire a permanent replacement.

The Wall Street Journal reported earlier on Friday, citing people familiar with the matter, that private-equity firms seeking to acquire just under 20 percent of Yahoo were working on new offers for a smaller stake at a higher valuation per share.

TPG Capital, which sources previously told Reuters had also bid for a minority stake, did not respond to a request for comment. Representatives of Silver Lake and Microsoft declined to comment while an Andreessen Horowitz representative could not immediately be reached for comment.

"As previously announced, the board is evaluating various alternatives as part of its comprehensive strategic review process, all of which are designed to enhance shareholder value and promote growth and innovation at Yahoo," a Yahoo representative said.

"The board's process is open to all alternatives and has not restricted the range of various options or proposals in any way," he added.

The first offer by Silver Lake's consortium valued Yahoo at $16.6 per share, about $1 per share less than what TPG proposed, people familiar the matter had previously told Reuters. Yahoo shares closed down 1.3 percent at $14.96 on Friday.

Yahoo has several available options. Chinese online commerce giant Alibaba, in which Yahoo has a 40 percent stake, is preparing a $4 billion bank loan to buy back that stake, Thomson Reuters publication Basis Point reported on Thursday, citing sources.

But Alibaba could choose to partner with buyout groups Blackstone Group LP, Bain Capital, and Japan's Softbank Corp. for a full-out bid for Yahoo, sources familiar with the matter have previously told Reuters.

Private-equity firm Thomas H. Lee Partners is interested in buying the U.S. operations of Yahoo, people familiar with the matter have also told Reuters previously.

Yahoo's difficulty in competing with Internet heavyweights such as Google Inc. and Facebook have forced it to explore proposals to revamp its business. Yahoo has a market capitalization of $18.5 billion.

(Reporting by Greg Roumeliotis in New York, Alexei Oreskovic in San Fransisco and Bill Rigby in Seattle; Editing by Gary Hill)