Yahoo co-founder Jerry Yang and other board members have privately told four major private equity firms that the board would not support a takeover offer for the entire company, Fortune has learned. The message was then reinforced this morning, when Yahoo (YHOO) announced that the hiring of PayPal president Scott Thompson as its new CEO.

Today’s private equity firms are loathe to attempt hostile takeovers, meaning that board opposition could be a deal-breaker. They also like to install their own CEOs, and it’s unlikely that Thompson would accept the job without some assurances that he wouldn’t soon be shown the door by a new owner.

The four firms are: Bain Capital, The Blackstone Group (BX), Silver Lake Partners and TPG Capital. Bain and Blackstone had originally been working with China’s Alibaba Group and Japan’s Softbank Corp., on a complicated acquisition that effectively would have left the PE firms with Yahoo’s U.S. assets (Alibaba and Softbank would have taken the Asia assets).

Since then, however, Alibaba and Softbank have also offered to acquire the Asian assets while leaving the U.S. business alone — a $17 billion proposal that Yahoo’s board is (slowly) considering.

An Asian divestiture could leave Bain and Blackstone trying to buy the U.S. assets solo. Silver Lake and TPG also are said to each be interested in such a deal, after previously having offered to acquire minority stakes in Yahoo via a PIPE (private-into-public-equity) transaction.

But, again, Yahoo has told each of the private equity firms to back off. This could all change later this month if Dan Loeb is able to get some of his (to be) proposed directors on Yahoo’s board, or if the Asia divestiture deal collapses. For now, however, a Yahoo buyout is highly unlikely.

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