AOL Inc. and several private-equity firms are exploring making an offer to buy Yahoo Inc., according to people familiar with the matter, devising a bold plan to marry two big Internet brands facing steep challenges.

Silver Lake Partners and Blackstone Group LP are among the firms that have expressed interest in teaming up with AOL to buy Yahoo or trying to take it private on their own, these people said. They added that at least two or three other firms could be interested in participating if a formal buyout proposal is drawn up.

The people familiar with the matter cautioned that these discussions—involving private-equity firms, AOL executives and financial advisers—are preliminary and don't yet involve Yahoo. The conversations may not lead to an approach given the complexities in structuring a proposal, the people said.

Spokeswomen for Yahoo and AOL declined to comment.

AOL, which spun off from Time Warner Inc. in late 2009, currently has a market capitalization of $2.68 billion, far smaller than Yahoo's $20.56 billion market value.

Shares of Yahoo jumped 13% to $17.23 in after-hours trading Wednesday, after rising 5.7% to $15.25 at 4 p.m. on the Nasdaq Stock Market. The stock traded 49.6 million shares in the regular session, compared with an average of 17 million shares a day so far this month. It was one of the best-performing tech stocks of the day.

One of the scenarios under discussion among the buyout firms is a complex deal in which China's Alibaba Group would buy back Yahoo's roughly 40% stake in Alibaba, the people said.

Some of Yahoo's other assets would also be sold off to interested media or technology companies, and the remaining company would be of a much smaller valuation that private-equity firms could get financing for, one of the people said.

Another scenario involves AOL combining its operations with Yahoo in a reverse merger after Yahoo disposes of the Alibaba stake, the people said. It is unclear if the resulting entity would be listed publicly.

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