The president, who threatened to fire Mr Powell earlier this year before U-turning on that course this month, has consistently demanded the Federal Reserve cuts interest rates to help bolster economic growth.
But the central bank has held off since Mr Trump’s second term in office began, citing threats to the pace of price growth from his on-off trade war.
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By raising tariffs on imports in a bid to boost American jobs and make US-produced goods more competitive, Mr Powell believes the spectre of inflation is looming over the world’s largest economy.
But the official inflation figures are yet to show any marked increase from rising import costs.
“I know within three or four people who I’m going to pick,” Mr Trump said in remarks to reporters while on his visit to Europe for the NATO summit at The Hague.
He said Mr Powell, the Fed chair, was “an average-minded person” with a “low IQ for what he does”.
“I think he’s a very stupid person, actually,” he added.
US media suggest the contenders to succeed Mr Powell include former Fed governor Kevin Warsh, National Economic Council head Kevin Hassett, current Fed governor Christopher Waller and Treasury Secretary Scott Bessent.
The Fed chair is not due to leave his position until May next year.
The Federal Reserve, like the Bank of England in the UK, is independent of government.
Mr Trump is desperate to grow the US economy after a sharp slowdown in the first quarter of the year was blamed on the threat of his trade war and early salvoes.
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What’s behind the Trump-Powell spat?
Analysts see Mr Trump’s on-off criticism of Mr Powell as an attempt to influence monetary policy through the back door.
The prospects of a battle to remove him has previously rattled financial markets.
For his part, Mr Powell told a Congressional hearing on policy on Tuesday that higher tariffs from the trade war could push up inflation this summer – a time when the Fed has already indicated it could move to cut its target range for interest rates.
