(Recasts with conclusion of interviews)
WASHINGTON, Oct 19 (Reuters) - President Donald Trump has concluded interviews with the five candidates he is considering to chair the Federal Reserve and could announce a decision as early as next week, a source familiar with the process said on Thursday.
Trump met with current Fed chair Janet Yellen on Thursday. That meeting "went well," the source said, adding that Trump had not made up his mind one way or the other about his list.
"I don't think he's leaning yet," the source said.
Other contenders to lead the U.S. central bank are top Trump economic adviser Gary Cohn, Fed Board Governor Jerome Powell, former Fed governor Kevin Warsh and Stanford University economics professor John Taylor.
Powell, who is viewed as representing a continuation of Yellen's gradualist approach to raising interest rates, along with Warsh, are seen as the top contenders.
Despite his time as Fed Governor under Chair Ben Bernanke, Warsh is seen as a less well-known nominee. He has criticized the Fed's bond-buying program and advocated changes in its inflation target.
U.S. Treasury yields briefly renewed their drop late Thursday after Politico reported that Trump was leaning toward nominating Powell for the job.
Trump leaves on Nov. 3 for a tour of Asia and is expected to announce his choice before that trip.
The president told reporters on Tuesday that he likes all five candidates. Ill make a decision over the next fairly short period of time, Trump said.
Meanwhile, a member of the U.S. House of Representatives' Freedom Caucus mounted a campaign to kill any chance of a second term for Yellen, the latest sign conservative Republicans want a fresh face at the helm of the Fed, which sets U.S. monetary policy.
Representative Warren Davidson, a Republican on the House Financial Services Committee's monetary policy panel, is among those who want a change. He is circulating a letter opposing Yellen's reappointment, the Ohio congressman's spokesman said.
"Davidson is very passionate about this process," the spokesman said, adding that the lawmaker is particularly concerned about the impact Fed policy has had on the ability of small firms to raise operating funds.
Members of the Freedom Caucus, the most conservative Republican grouping in Congress, have been critical of Yellen, with some accusing her of keeping monetary policy too loose.
Key members of the House Financial Services Committee also have backed ideas proposed by contenders to replace Yellen. Taylor's research, for example, figured prominently in a House-passed bill requiring the Fed to explain its actions through a strict set of rules.
The House, however, has no direct control over the appointment of a Fed chief. The Senate decides whether to confirm the president's nominee.
Trump has criticized Yellen in the past and vowed to "drain the swamp" in Washington by naming new people to top jobs and embracing different ideas. But his economic agenda could benefit from the steady economic conditions fostered by Yellen's Fed.
Cohn's chances of getting the job were thought to have dimmed after he publicly criticized the president's response to a white supremacist rally in Virginia.
But the top White House economic adviser, who is helping to lead the administration's push for tax reform, has since gotten back into Trump's good graces. (Additional reporting by Howard Schneider; Editing by Paul Simao and James Dalgleish)