Fischer, 70, is known to have coached top economists and financial leaders, including current Fed Chairman Ben Bernanke and European Central Bank's Mario Draghi. He stepped down as head of the Bank of Israel in June and has formerly worked at the World Bank and International Monetary Fund.
He has voiced concern about the Fed's current forward guidance policy, which implies central banking actions as much as two years in advance, though he also said the policy has worked thus far.
Economists consider Fischer an ideal fit for the job due to his extensive central banking expertise, as well as his agreement with Yellen's policy initiatives. White House advisers seek someone with financial crisis management experience, and Fischer has plenty.