By Andrea Shalal and Howard Schneider

WASHINGTON (Reuters) -U.S. President Donald Trump said on Tuesday he will decide on a nominee to fill a coming vacancy on the Federal Reserve's Board of Governors by the end of the week, and had separately narrowed the possible replacements for Fed Chair Jerome Powell to a short list of four.

"I'll be making that decision before the end of the week," Trump said of his plans to name a replacement for Fed Governor Adriana Kugler, who last week unexpectedly announced she was leaving as of this Friday to return to her academic position at Georgetown University.

Trump, in comments to reporters at the White House, distinguished between picking Kugler's replacement for a term that only lasts until January, and the selection of Powell's replacement once he leaves the top Fed job in May.

But with the Fed board's other seats occupied with people, including Powell, whose terms run for years longer, Trump's choice of Kugler's replacement could have implications for his selection of a chair, a process Trump said has been narrowed to economic adviser Kevin Hassett, former Fed governor and Trump supporter Kevin Warsh, and two other people. Trump did not name those people, but one is thought to be current Fed Governor Christopher Waller.

"We're also looking at the Fed chair, and that's down to four people right now ... Two Kevins and two other people," Trump said. 

Trump earlier in the day said in an interview with CNBC that he had removed Treasury Secretary Scott Bessent from consideration for Fed chair because Bessent wanted to remain in the top Treasury job.

In the CNBC interview, Trump said Kugler's decision to vacate her seat early was a "pleasant surprise" that gives him an immediate opening to fill with a person who could also be promoted to take Powell's place.

Kugler's replacement would, at least initially, be appointed for just the few months remaining in Kugler's term.

But Trump could be explicit he plans for that person to then be nominated to a full 14-year term after that time, and to also be his choice to replace Powell, giving his nominee several months and several policy meetings to begin to influence the policy debate.

"A lot of people say, when you do that, why don't you just pick the person who is going to head up the Fed? That's a possibility too," Trump said in the CNBC interview.

The president has been critical of Powell for not cutting interest rates since Trump returned to power in January, and contemplated trying to fire him, even as Fed policymakers balance evidence of both a slowing economy and a weakening job market against the fact inflation remains well above the central bank's 2% target and is expected to move higher.

The Fed is charged by Congress to maintain stable prices and maximum employment, and is potentially facing a situation where the two goals conflict with each other, posing a painful set of tradeoffs.

The nominee to fill Kugler's seat will need to be confirmed by the Senate, and would require another Senate vote for a full 14-year term early next year. The nomination for the next Fed chief would require a separate Senate confirmation process.

James Fishback, the CEO of Azoria investment firm and a former advisor at efficiency department DOGE, spoke to Trump on Monday to pitch himself as a temporary Fed pick, and a presidential aide requested informative material from him, according to a source with knowledge of the interactions.

The White House did not immediately respond to a request for comment about Fishback.

'ANOTHER LEVEL OF PROBLEMS'

Kugler's departure was announced the same day Trump, angered over data that showed job growth slowing in the first months of his administration, fired Bureau of Labor Statistics Commissioner Erika McEntarfer while alleging without evidence that BLS was manipulating the jobs data to make him look bad.

Economists have warned since Trump returned to the White House in January that his combination of import tariffs and erratic trade policy would likely lead to a labor market slowdown and higher inflation, a broadly shared outlook that has been among the factors keeping the Fed from lowering rates until the inflation impact becomes clearer.

The central bank last week held its policy rate steady in the 4.25%-4.50% range, though Waller dissented on the grounds the inflation risk from tariffs appeared modest at best, while the job market and growth in general appeared to be weakening.

The release on Friday of the jobs report for July, with weak monthly employment gains and downward revisions to prior months, appeared to validate those concerns and led to increased market bets the Fed would cut rates at its September 16-17 meeting.

The firing of the BLS commissioner touched off a global wave of concern about the continued integrity of U.S. government data, with Trump's actions being given a fire-the-messenger interpretation by much of the economics and statistics community.

The president's choice now to head the statistics agency and potentially to lead the Fed will be scrutinized all the more carefully, said Michael Strain, director of economic policy studies at the conservative American Enterprise Institute.

"Imagine if one of your concerns is that there's a lackey in charge of the agency and the numbers are fake. That's ... another level of problems," Strain said of the BLS. "Maybe he sees this independence thing really matters. Maybe he's got somebody from the outside saying 'Look, Mr. President, if you appoint somebody who's perceived to be a lackey as the Fed chair, take the BLS freakout and multiply by 1,000."