In an interview at the World Bank/International Monetary Fund conference Friday, Fischer pushed the president to reappoint Janet Yellen as Fed chair. Though normally reluctant to wade into political waters, he made his preference known.
"He should appoint Janet Yellen," Fischer told CNBC in a live interview. "I'm not going to go into the rest of the list."
That list includes a handful of other candidates, at least two of whom are considered stronger bets than Yellen to assume the reins when her term expires in February. Current Fed Governor Jerome "Jay" Powell and former Governor Kevin Warsh are considered more likely bets.
Fischer said that Yellen has the right qualities for the job.
"Janet is a safe pair of hands and very good at explaining what she's doing and persuading people of what she's doing. I think it's important," he said.
Fischer also said he expects the Fed will be able to stick to the schedule it has penciled in, which calls for another rate hike in December followed by three more in 2018. Fed officials are hoping the economy remains strong enough to allow it to normalize policy after the measures it took as the U.S. recovered from the financial crisis.
"That's achievable if we continue to run good quality (data)," he said. "With the global economy coming up for the first time and having faster growth in the global economy than we expected, there's a good chance of that."
Fischer's resignation takes effect Friday, a move he announced in September, citing "personal reasons." His departure comes two days before his 74th birthday.
Former President Barack Obama nominated Fischer to the Fed in October 2014.
During his tenure, the central bank began its first steps toward policy normalization after the extreme accommodation it followed for years. The Fed has hiked its benchmark interest rate four times since December 2015 and is on track for one more hike in December.
The Fed this month will begin another historic process — the reduction of its $4.5 trillion balance sheet. The process will entail the Fed allowing some of the proceeds for the bonds it purchased during its stimulus efforts to roll off. The central bank is hoping that markets see little turbulence from the process.
The balance sheet reduction will be slow — just $10 billion a month will be allowed to roll off at first, a number that will increase $10 billion a quarter until it reaches $50 billion.
In an ideal world, Fischer said, the process would move more quickly.
"I wish the circumstances were such that going faster was the right policy," he said. "But given the uncertainty about the inflation rate approaching the 2 percent target, we have to be more careful than full speed ahead."