Bernanke was initially nominated to the post by President George W. Bush. Obama asked Bernanke to serve another term as chairman, which he began Feb. 1, 2010. The 59-year-old former Princeton University professor and Great Depression scholar served on Bush's Council of Economic Advisers.
Fed spokeswoman Michelle Smith declined to comment. A White House official declined to comment until the president has made a decision and is ready to announce it, adding that Obama's remarks were intended to express admiration for Bernanke.
The comments came on the eve of the two-day meeting of the Fed's policy-setting Open Market Committee. In recent months, Fed officials have debated whether to scale back their purchases of Treasury bonds as the economy extends its recovery.
"It's really hard to believe the next chairman would change the course of monetary policy," said Roberto Perli of Cornerstone Macro L.P. in Washington, a former economist for the Fed's division of monetary affairs.
At the same time, Perli said, "it doesn't help make the Fed's communications easier if Obama is talking about Bernanke in the past tense."
Though neither the White House nor Bernanke have said definitively that the chairman won't seek a third term, there have been signals he would like to leave. Bernanke broke with tradition and decided not to attend the Fed's annual conference in Jackson Hole, Wyo., this year.
"The odds of Bernanke staying on were pretty low," said Michael Feroli, chief U.S. economist for JPMorgan Chase & Co. in New York. "This will confirm one aspect of the story and allow people to think of the other scenarios - somebody else will be taking the helm."
Bernanke said in March that he's "spoken to the president a bit" about his future and felt no personal responsibility to stay at the Fed and oversee the reversal of its policies.