* Fischer, former Bank of Israel chief, would be Fed's No. 2
* Final votes on Fischer, Brainard, Powell set for Thursday
* White House eyes community bankers for another slot (Recasts with results of Senate votes, background on potential future nominees)
WASHINGTON, June 10 (Reuters) - Stanley Fischer's nomination to be vice chairman of the U.S. Federal Reserve advanced in the Senate on Tuesday, along with two other nominees to the U.S. central bank, setting the table for their expected confirmation later this week.
The former governor of the Bank of Israel, who was separately confirmed to a Fed board seat last month, is widely expected to win approval for a concurrent four-year term as the Fed's No. 2 when the Senate votes on Thursday.
The Senate agreed 56-38 to limit debate on his nomination, setting the clock ticking toward final confirmation.
The nomination of former U.S. Treasury official Lael Brainard for a board seat and the renomination of Fed Governor Jerome Powell for a fresh board term moved forward on similar tallies. They, too, will face final votes starting at 1:45 p.m. (1745 GMT) on Thursday.
Fischer, a widely respected economist with extensive policymaking experience, is expected to play an influential role in helping to shape U.S. monetary policy, and could prove a powerful ally of Fed Chair Janet Yellen.
While Fischer was sworn in as a member of the Fed board on May 28, Brainard's expected arrival would be another boost to the central bank's depleted ranks as policymakers map out plans to exit from their extraordinary monetary stimulus.
The central bank is winding down its massive bond-buying program and it is expected to lift benchmark overnight interest rates from zero sometime next year.
Officials, who hold their next policy meeting on June 17-18, are divided over the degree to which a sharp drop in the U.S. unemployment rate marks an evaporation of economic slack, and are debating how quickly to raise rates.
During a Senate hearing in March, Fischer broadly endorsed the Fed's current direction, and indicated he felt there was still ample room - as Yellen has suggested - to maintain loose monetary policy to boost employment.
Even if the nominees are confirmed, President Barack Obama would still have two seats to fill on the normally seven-member Fed board.
For one of the seats, the White House is considering tapping someone with community banking experience.
Sources have said Diana Preston, a lawyer who recently left a post at the American Bankers Association, New Mexico banker Rebeca Romero Rainey and Ann Marie Mehlum, who headed an Oregon-based bank before joining a federal small-business agency last year, have come under consideration.
At the Bank of Israel, Fischer was credited with ably steering Israel's economy through the financial crisis. He also served as an executive at Citigroup and as the No. 2 official at the International Monetary Fund, where he helped lead the effort to combat Asia's financial crisis in the 1990s.
Brainard, who served as a top financial diplomat at the Treasury until late last year, was involved in bank regulation talks with European officials during the height of the euro zone financial crisis. She also worked at the White House during the Clinton administration.
Powell, who previously worked as a lawyer and an investment banker, served in senior Treasury posts under President George H.W. Bush. (Reporting by Michael Flaherty; Additional reporting by Tim Ahmann; Editing by Chizu Nomiyama and Andrea Ricci)