Bernanke is widely expected to step down when his term expires in January 2014.
Former Treasury Secretary Larry Summers recently withdrew from consideration as Bernanke's successor, explaining he anticipated a contentious nomination process if he were chosen.
That left Fed Vice Chair Janet Yellen as the front-runner for the position.
The New York Times reported Thursday Buffett, in an interview, said he did not know Yellen and he would prefer Bernanke to stay in his job for a third term.
"I think if you've got a .400 hitter in the lineup, you don't take him out," Buffett said, although he also acknowledged President Obama was not likely to ask Bernanke to stay on the job.
"I don't have a second choice," he said.