Obama told Charlie Rose, host of a PBS interview program, that Bernanke was like longtime FBI Director Robert Mueller, who agreed to stay two years longer in the job than he had planned and is to leave in the coming months.
"Well, I think Ben Bernanke's done an outstanding job," Obama said. "Ben Bernanke's a little bit like Bob Mueller, the head of the FBI—where he's already stayed a lot longer than he wanted or he was supposed to."
Asked whether he would reappoint Bernanke if he wanted to stay on at the Fed, Obama did not answer directly.
If history is any guide, Obama will pick a candidate to succeed the one-time Princeton University professor sometime during the summer, allowing ample time for the Senate to consider the nominee before a final confirming vote.
Here is a quick look at the likely leading choices:
Yellen, 66, has been Fed vice chair since 2010 and is viewed as a strong contender to be the next Fed chair. A Reuters poll on June 12 found that an overwhelming majority of economists predicted she would get the job.
Yellen has been a forceful advocate of the aggressive steps taken under Bernanke to spur economic growth, earning her a reputation as a policy "dove" who would tolerate a bit more inflation to drive down unemployment that she deemed too high.
(Read More: Obama: Bernanke at the Fed 'Longer Than He Wanted')
If picked to succeed Bernanke, she would become the 100-year-old central bank's first female chief. Before her current post, Yellen was president of the Federal Reserve Bank of San Francisco. She was chairman of the White House Council of Economic Advisors under President Bill Clinton and a Fed Board governor in Washington from 1994 to 1997.
A former professor at the University of California, Berkeley, Yellen has high standing among other academics. She began her career as an assistant professor at Harvard University in the early 1970s before shifting to the Fed.
Summers, 58, is a Harvard economist who was Obama's first National Economic Council director, a post within the president's inner circle. He also was Clinton's Treasury secretary after holding other senior posts in the department.
Viewed as brilliant but prickly, Summers was a full Harvard professor by the age of 28 and later became president of the university. But his nomination might be controversial, in large part because of his reputation for rubbing people the wrong way.
In a notable episode in 2005, he was heavily criticized for suggesting there were fewer women than men in science and engineering because of a lack of aptitude. Many saw the remarks as sexist; Summers said he was trying to stimulate debate.