By Steven Scheer and Jonathan Spicer

(Reuters) - Stanley Fischer, who led the Bank of Israel for eight years until he stepped down in June, has been asked to be the Federal Reserve's next vice chair once Janet Yellen takes over as chief of the U.S. central bank, a source familiar with the issue said on Wednesday.

Fischer, 70, is widely respected as one of the world's top monetary economists. He is seen as a pragmatic policymaker and has praised the Fed's extraordinary steps to boost the U.S. economy. At the Massachusetts Institute of Technology, he once taught current Fed Chairman Ben Bernanke and Mario Draghi, the European Central Bank president.

Yellen, the Fed's vice chair, is expected to win approval from the U.S. Senate next week to take the reins from Bernanke, whose term ends in January.

Fischer, who was born in Zambia and has Israeli and U.S. dual citizenship, would also need Senate approval if he accepts the offer from the White House. "He's been offered the job" said the source, who declined to be named.

The White House declined to comment. A Fed spokeswoman said the White House was responsible for nominations.

Fischer, who could not immediately be reached, has held top-level posts at the World Bank and the International Monetary Fund, and was credited with guiding Israel through the global economic crisis with minimal damage. For the Fed, he would bring the fresh perspective of an outsider, especially on communications, yet offer some continuity too.

He is "difficult to characterize with a term as obtuse as 'hawk' or 'dove' because he takes a balanced, academic approach to various topics of debate," said Thomas Simons, an economist at brokerage Jefferies.

"However, given that he played an instrumental role in helping Ben Bernanke form his views on monetary economics, his presence at the Fed would represent some consistency in this time of transition."

Fischer would arrive at a U.S. central bank starting to navigate a return to normalcy after taking dramatic and unprecedented steps to emerge from the Great Recession of 2007-2009.

The Fed is now wrestling with the decision of when to scale back its huge bond-buying program that sought to drive down long-term borrowing costs and swelled its balance sheet to some $4 trillion. It buys $85-billion a month in Treasuries and mortgage bonds in its current, third round of "quantitative easing," or QE3.

At an IMF economic forum on November 8, held in Fischer's honor, he suggested he is a strong believer in the effectiveness of the Fed's unconventional policies.

"It's very hard to reach the conclusion that the unorthodox measures are ineffective," Fischer said of the bond buying, acknowledging the policy is controversial.

"They appear to be effective and they essentially do that by working off either the provision of liquidity in markets where liquidity has effectively dried up, or by changing interest rates other than the central bank interest rate," he said on a panel seated next to Bernanke.

As Fed vice chair, Fischer would have a strong hand in shaping policy. Yellen, who has held the post since 2010, was a driving force behind the Fed's adoption last year of an inflation target, an important policy milestone for the bank.

One possible source of tension may be how to telegraph the Fed's policy intentions. While Yellen and Bernanke have tied a rate rise to future levels of unemployment and inflation, Fischer has publicly warned about central banks giving so-called forward guidance that is too precise.

"He's going to think outside of the box, he's going to push the Fed a little bit, and that's not a bad thing," said Diane Swonk, chief economist at Mesirow Financial in Chicago.

Fischer "is very cognizant of what you can and can't communicate, and I'm not sure the Fed is always so sensitive about that."

Bloomberg News and Israel's Channel 2 earlier reported Fischer as the front runner for Fed vice chair.

If he takes the job, it would be the second time this year a major central bank made a high-profile hire from abroad. The Bank of Canada's chief Mark Carney earlier this year became the first foreigner to lead the Bank of England.

'NEARING A DECISION'

The Fed's seven-member board is depleted and risks thinning further. Elizabeth Duke stepped down in August, Sarah Raskin is set to leave for a job at the U.S. Treasury, and Bernanke is expected to depart when his term as chair expires January 31.

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