After eight years in the trenches with "people beating the crap out of him," Federal Reserve Chairman Ben Bernanke "deserves a break," former Fed Governor Frederic Mishkin told CNBC on Tuesday.
But he added the central bank's decision on when to start tapering its bond-buying program "will not be affected" should Bernanke choose to leave at the end of his term.
In an interview that aired Monday, President Barack Obama hinted that Bernanke may be on his way out. "Ben Bernanke's done an outstanding job," the president said in the interview with Charlie Rose.
But when asked whether he would reappoint Bernanke if the Fed chief wanted to keep the job, Obama did not answer directly. "He's already stayed a lot longer than he wanted."
Any changing of the guard at the Fed would come at a complex time for policymakers who are grappling with deciding on when to scale back the central bank's $85 billion-a-month asset purchases known as quantitative easing. Investors are hoping for some answers when Bernanke holds a news conference on Wednesday afternoon, following the Fed's two-day meeting, which began on Tuesday.
(Read More: Why Some Traders View Fed Tapering as Tightening)
To cynics who say Bernanke might speed-up tapering before abandoning ship, Mishkin said in a "Squawk Box" interview that if the Fed chairman is indeed planning on leaving, he would not "do policy in terms of how it looks for him personally."
"If, in fact, he thinks it's appropriate to not taper, that's what he would do," Mishkin said. "If he thinks it's appropriate to taper faster, that's what he's going to do. It will not be affected."
With Bernanke's second term expiring at the end of January, that would be a natural time for him to leave, Mishkin said. "Eight years is really long enough for a chairman. Ben, very importantly, doesn't want to stay too long. I think that was a serious mistake on Greenspan's part."
Alan Greenspan served as Fed chairman under four presidents for 18-plus-years. If Greenspan "could have figured out a way to stay he would have," Mishkin quipped.
(Read More: Greenspan: Taper Now, Even If Economy Isn't Ready)
On the other hand, Bernanke—who took over as Fed chairman after Greenspan retired in 2006—is not in love with his job, Mishkin said. "He's put in his eight years. It's been exhausting for him. He knows he did the best job he possibly could."
"Given the circumstances he was handed, it's quite extraordinary what he's been able to do," Mishkin said, crediting the Fed chairman with helping prevent "the real potential of another Great Depression, not just a recession."
But he added that's it not like "[Bernanke] can't leave because nobody else can do the job. The organization is very a strong one."
Obama is said to be considering Fed Vice Chairwoman Janet Yellen for the job, as well as former Obama and Clinton aide Lawrence Summers and former Treasury Secretary Timothy Geithner, among others.
An announcement could come as early as this fall, to give the Fed nominee time to get through Senate confirmation by the time Bernanke's term is up.