The company has this summer faced the collapse of two hedge funds, asset writedowns and poor trading results, amid declines in subprime and other mortgages. Third-quarter profit slid 61 percent, although Bear said it believed the worst was over. The shares trade at about 1.3 times book value.
Bear Stearns' $850 million Asset-Backed Securities Fund experienced declines in July, prompting some investors to seek redemption of their investments.
The investment bank, however, believes the assets in the fund -- tied to Alt-A and prime mortgages -- are worth more than what current market conditions will allow.
"I'm not certain why Bear would want to sell a piece of itself at an impaired value," Brad Hintz, an analyst at Sanford C. Bernstein, told Reuters.
"This management team has gone its own way for too many years to suddenly decide it wants to sell out at a low valuation. It's a fine franchise that just went through a very difficult environment, but fixed-income problems don't last forever."
Buffett seeks out undervalued companies and has invested in Wall Street before. He took a 12 percent stake in the former Salomon Brothers in 1987 to help defend the brokerage from the advances of financier Ronald Perelman.
Buffett became interim chairman in 1991 to help Salomon clean house following a Treasury market scandal. Nonetheless, the investment itself was not one of Buffett's best.
"If it's Buffett, it would be a classic example of him exploiting other people's folly," said Chuck Carnevale, chief investment officer at Great Companies LLC, which invests $400 million. "If markets eventually correct themselves, the subprime disaster goes away and Bear is still standing, there's an enormous amount of potential upside."
- Reuters contributed to this report.