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Do markets really just want Bernanke to stay?

Ben Bernanke
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As Federal Reserve chairman Ben Bernanke's term edges closer to its end and speculation over who will replace him grips markets, some industry watchers say the best option is for Bernanke not to leave at all.

Billionaire investor Warren Buffett told CNBC on Thursday that Bernanke should get the chance to finish what he started.

"If you have a '.400 hitter' in the line-up, you don't take him out," Buffett told CNBC in a joint television interview with Brian Moynihan, chief executive of Bank of America, which aired on Thursday.

(Read more: Fed's taper surprise puts jumpy market in limbo)

"He may want to leave, but I think… since the panic of five years ago… he's done a terrific job and I think he ought to get a chance to play out a little more of his hand," he added.

During Bernanke's two terms as Fed chairman he has embarked on one of the most aggressive quantitative easing programs the world has ever seen. Many industry watchers have applauded the American economist for his success in helping drag the U.S. economy out of its worst recession since the 1930s.

But despite his popularity, it had been widely accepted that he would leave at the end of his second term on January 31, with reports showing he has already stayed much longer than he wanted to.

However, this week, news that controversial candidate Larry Summers had withdrawn his name for consideration to be the next Fed chairperson has stirred up the debate again. Vice chair Janet Yellen is widely seen as the key contender, but some commentators say Summers' bowing out has prompted whispers that Bernanke might be in the running again after all.

(Read more: Rick Santelli: How will history judge Ben Bernanke?)

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Jack Bouroudjian, CEO of Bull and Bear Partners, told CNBC's Asia Squawk Box on Friday that markets would respond well to Bernanke remaining as Fed chair because what they really crave is certainty.

"What I worry about is that we have got a doctor in the middle of a surgery and we are pulling him out…right in the middle," he said.

"So what we want to do is see a little bit of certainty, that would probably be the thing that would help this market more than anything else," he said, adding that in his view, keeping Bernanke at the helm would be the only way the Fed could control interest rates as it unwinds its $85 billion a month bond buying program.

"The reality is there is a chance that [Bernanke] might [stay]. I know that people have been talking about it; there are whispers on the floor of the exchange that he might," he added.

(Read more: What Bernanke's successor needs)

This week CNBC reported that Tony Fratto, former White House press secretary in the George W. Bush administration, had said keeping Ben Bernanke was still a possibility.

"I think one choice nobody has really talked about, which I really believe is still a possibility until someone rules it out, is that you keep the best guy for the job in the job—that's Ben Bernanke," said Fratto.

The U.S. central bank surprised markets on Wednesday with its decision not to begin tapering its asset purchases, despite broad expectations of a $10-$20 billion reduction in its monthly asset purchases.

—By CNBC's Katie Holliday: Follow her on Twitter @hollidaykatie