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Silver Lake Partners and Blackstone Group LP are interested in teaming up to purchase Web portal Yahoo, according to a report by the Wall Street Journal.

Yahoo has been under pressure to improve its performance since Carol Bartz was appointed CEO in 2009. Bartz herself has come under criticism for mishandling relationships with important partners in Asia and allowing high turnover in Yahoo’s executive ranks.

If AOL, Silver Lake Partners and Blackstone LP do not team up, the private equity firms would reportedly be interested in buying the company on their own and taking it private. There are also three other unnamed private equity firms that may be interested in making a deal with Yahoo, according to the report.

It isn’t clear how big of a player AOL would be in the deal — it’s current valued at $2.7 billion, and reported operating income of $166.6 million in its most recent quarterly filing with the Securities and Exchange Commission. (It took a $1 billion goodwill-impairment charge in the quarter.) AOL has $391.6 million in cash, according to the filing.

Yahoo, on the other hand, is worth $20.6 billion, and reported net income of $143 million in its most recent quarter.

Yahoo has not participated in the discussions yet, according to the Wall Street Journal report. One option would be a “reverse merger” — in which Yahoo and AOL combine their operations after Yahoo sheds its valuable stake in Alibaba Group, a Chinese e-commerce concern that runs business trading and online retail sites and operates Yahoo China, according to reports. The other involves Alibaba Group repurchasing Yahoo’s 40 percent stake in the company, and Yahoo selling off various other assets to make it easier to purchase by private firms.

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