WASHINGTON — Stanley Fischer, the former governor of the Bank of Israel and a mentor to the Federal Reserve’s chairman, Ben S. Bernanke, is the leading candidate to become vice chairman of the Fed, according to former and current administration officials.

If nominated, and then confirmed by the Senate, Mr. Fischer, 70, would succeed Janet L. Yellen, whom President Obama nominated to succeed Mr. Bernanke as the Fed’s leader when his term ends in January.

Mr. Fischer is at once a surprising choice and a popular pick among economists and investors. He is a highly regarded economist with significant policy-making experience, yet many had considered his selection improbable because of his recent service in a foreign government. News about Mr. Fischer’s possible nomination was reported on Israeli television.

That experience could become a concern if he is nominated, as could his experience at Citigroup, where he was vice chairman between 2002 and 2005. The company’s expansion during that period eventually ended in a federal bailout.