China's Alibaba Group and Japan's Softbank are in talks with private equity firms about making an unsolicited bid for Yahoo!, according to the Bloomberg financial news agency.

The bid would be for all of the Sunnyvale, California-based Yahoo!, Bloomberg reported, citing people with knowledge of the matter.

Yahoo!, which has been rumored to be on the block since the firing of chief executive Carol Bartz in September, would prefer to sell a smaller stake rather than the entire company, the news agency said.

One scenario would have Softbank and Alibaba buying back the stakes that Yahoo! owns in the companies and a private equity firm supplying the remaining funding needed to buy Yahoo!, Bloomberg said.

Various press reports in recent weeks have cited Texas Pacific Group, ProvidenceEquity Partners, Silver Lake Partners, KKR, Bain Capital and Blackstone as among the private equity firms interested in a Yahoo! deal.

Yahoo! owns a 40-percent stake in Alibaba and is a partner with Softbank in Yahoo! Japan. Yahoo! owns 35 percent of Yahoo! Japan.

Alibaba chairman Jack Ma, who had a strained relationship with Bartz, has expressed interest in buying all or part of Yahoo! on several occasions.

Bank of America Merrill Lynch analyst Justin Post said Wednesday that Alibaba and Softbank and private equity or bank partners would be "the most logical buyers of Yahoo!"

"Anyone else buying Yahoo! would own 40 percent of Alibaba Group and Alibaba Group could create major issues for a buyer if they are not part of the deal," Post added.

The relationship between Yahoo! and Alibaba was strained earlier this year in a dispute over Alibaba's online payments platform Alipay.

Yahoo! was once an Internet powerhouse but has struggled recently to build a profitable, growing business out of its still huge Web audience.

Microsoft tried to buy the company for $44.6 billion in February 2008 -- a per-share price of $31 -- but Yahoo! said that the bid undervalued the company, and even reportedly turned down a higher, second offer of $32-33 a share.

Yahoo! shares lost 0.31 percent to close at $15.92 on Wall Street on Wednesday.