The New York Times, citing unnamed people briefed on the discussions, said Bear Stearns is in serious talks to sell up to a 20 percent stake.
Other investors that expressed interest include Bank of America, Wachovia and two Chinese banks: China CITIC Bank Corp. and China Construction Bank, the newspaper said, citing the people.
The news sent Bear Stearns shares up $8.76, or 7.7 percent, to close at $123 on the New York Stock Exchange. They remain down 24.4 percent this year.
"When you have a sophisticated investor and the second wealthiest person in the universe interested in Bear Stearns, then this may be signaling that the company may be about to turn the corner," Clearbrook Financial Chief Investment Officer Tom Sowanick told Reuters, referring to Buffett.
A Bear Stearns spokesman declined to comment to CNBC on a potential deal. Berkshire Hathaway, Buffett's investment firm, never comments on any activities beyond what the Securities and Exchange Commission requires.
An outside investment would bolster Bear and its embattled chief executive, James Cayne.
"I think it's absolutely necessary because Bear Stearns was in deep trouble," Richard Bove, an analyst at Punk Ziegel, told CNBC.
Bove upgraded Bear Stearns shares to "market perform" from "sell" on Wednesday.
"About six weeks ago, we made the argument that the company had to be taken over, and watching the stock price over the last few hours, the stock was supposed to be going down but was actually going up, so it was apparent that something was going on," Bove said.
Hedge Fund Troubles Plague Bear Stearns
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.