The bank, which has been hit by the credit crisis, saw its shares rise by 14 per cent following the news that Mr Buffet could be about to buy.
Reports suggest that Mr Buffet is in talk with the chairman of Bear Stearns, Jimmy Cayne, over a possible 20 per cent share in the bank.
Shares in the bank climbed by $17.7 as a result of the rumours but at $123 a share they are still off the $145 price they held in June.
British trading billionaire, Joseph Lewis, bought up seven per cent of Bear Stearns earlier in the month for $860 million, the bank subsequently revealing 62 per cent losses in profits which totalled $171 million.
Mr Buffet is the world's third richest man with fortunes totalling about $52.5 billion so investment would be a sign of confidence in the bank.