AOL Inc. and several private equity firms are exploring the possibility of buying Yahoo Inc., according to people familiar with the matter.

Shares of Yahoo jumped more than 9 percent on Thursday on the news, fueled by the prospect that the Internet company could be the target of a buyout by private equity firms, possibly in conjunction with another media company like AOL or News Corp.

Silver Lake Partners and Blackstone Group LP are among the firms that have expressed interest in either teaming up with AOL to buy the company 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 very preliminary and don’t yet involve Yahoo. The conversations may not even lead to an approach given the complexities inherent in structuring a proposal, the people said.

Spokeswomen for Yahoo and AOL declined to comment. Blackstone also declined to comment. Silver Lake didn’t immediately respond to requests for comment.

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 the company, 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 or taken private. 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.