WASHINGTON (Reuters) -U.S. President Donald Trump's short list of candidates to succeed Jerome Powell as chair of the Federal Reserve now includes his aide Kevin Hassett, former Fed Governor Kevin Warsh and current Fed Governor Christopher Waller.

Trump told reporters at the White House that the three men were the finalists for appointments to the Fed, adding he would consider Scott Bessent, too, but that the Treasury secretary was not interested.

Bessent, who was with the president in the Oval Office, confirmed his lack of interest.

"I had four," Trump said. "Now I'm talking about three. He (Bessent) told me: 'I'm not leaving'."

The president has made clear he intends to install a Fed leader more aligned with his push for rapid interest-rate cuts, browbeating Powell for being "too late" to act on borrowing costs and for hurting home buyers with higher mortgage rates.

Powell's Fed has kept rates on hold all year on concern that Trump's tariffs could reignite inflation, although recently his concerns have shifted to center more on the slowing labor market.

The choice of a Fed chair will carry high stakes for financial markets, which closely watch Fed leadership changes for clues about the direction of interest rates, inflation policy and the central bank's independence.

U.S. job growth weakened sharply in August and the unemployment rate increased to nearly a four-year high of 4.3%, the Labor Department said on Friday, confirming that labor market conditions were softening.

Powell last month noted downside risks to the labor market that "may warrant" a careful policy adjustment, remarks that financial markets and analysts took to mean he would likely support a quarter-point interest-rate cut in September.

That's far short of the several percentage points of cuts that Trump has demanded.

Hassett, the director of the National Economic Council, has been a reliable advocate for Trump's tariffs and other policies, and agrees with Trump that the Fed has kept rates inappropriately high.

Warsh has repeatedly called for "regime change" at the Fed.

Waller, who ran the St. Louis Fed's research department before Trump picked him to be Fed governor in 2020, would be an institutionalist pick.

Bessent released a barrage of criticism against the Fed on Friday and called for a full review of the central bank's operations, from staffing to research to monetary policy.