President Trump showed off a draft of a letter firing the chair of Federal Reserve, Jerome H. Powell, during a meeting with roughly a dozen House Republicans on Tuesday night, polling them as to whether he should do it and indicating that he likely would, according to two people briefed on the meeting.

It remains to be seen whether Mr. Trump will actually go ahead with trying to fire Mr. Powell, a move that some in his administration have cautioned could be calamitous and have far more expansive fallout than the president appears to anticipate.

The meeting in the Oval Office was on an unrelated topic — the House members’ apprehensions about a crypto-related piece of potential legislation. But Mr. Trump used the meeting to discuss what has become one of his favorite topics: his hatred of Mr. Powell, whom he elevated to chair in 2017, during his first presidency.

Speaking from a separate meeting in the Oval Office on Wednesday, Mr. Trump confirmed that he had queried House lawmakers about whether he should fire Mr. Powell but said he had no imminent plans to do so.

“I talked about the concept of firing him. I said, ‘what do you think?’ Almost everyone of them said I should,” Mr. Trump said, adding “but I’m more conservative.” Mr. Trump, who often reflexively disputes news reports about his actions, said he hadn’t had a letter drafted.

Mr. Trump has been increasing his angry rhetoric around Mr. Powell — whom he attacks for not cutting interest rates while overseas counterparts have done so — for the past several days. He has seized on renovations that are underway at the Fed to refurbish a nearly 100-year-old building that will eventually house most of the central bank’s staff.

Asked later whether he would rule out firing the Fed chair, he said “I don’t rule out anything but I think it’s highly unlikely unless he has to leave for fraud." Mr. Trump then pointed to the Fed’s renovation, saying “I mean it’s possible there’s fraud involved with the $2.5 billion renovation.”

The project, which has been ongoing since 2021, has been scaled back because of swelling costs. The renovations are estimated to cost more than $2 billion once completed and are already tracking $700 million over budget.

The president has in recent weeks called on Mr. Powell to resign, saying he has not done enough to lower interest rates.

Some advisers to and allies of Mr. Trump insisted before he addressed reports about the meeting with House members that he’s simply trolling Mr. Powell and hoping to torment the Fed chair but won’t actually follow through with trying to fire him.

But the existence of the letter — and Mr. Trump’s interest in discussing it with the House members — suggests that the president is engaging in the type of moves that he often does ahead of ultimately making a major decision.

Representative Anna Paulina Luna, Republican of Florida, posted on the social media website X while the meeting was going on that, “Jerome Powell is going to be fired. Firing is imminent.”

A White House spokesman did not immediately respond to a request for comment. A spokesman for Ms. Luna did not immediately respond to an email seeking comment.

One person close to Mr. Trump said that despite that social media post, no move by the president is imminent and that Mr. Trump — as he often does — could pull back and simply be content to unleash attacks on Mr. Powell through his allies and administration officials.

CBS News previously reported that Mr. Trump has asked House lawmakers if he should fire Mr. Powell.

Mr. Trump’s focus on firing Mr. Powell — something he’s previously said publicly he won’t do — has come as he is trying desperately to move past anger from his own supporters at his administration’s refusal to disclose more about what is in files related to Jeffrey Epstein, the late financier and sex trafficker.

Mr. Trump’s attacks on the Fed have primarily been directed at Mr. Powell, who he has branded a “major loser,” a “numbskull” and a “stubborn mule,” among a range of other insults. He has also floated naming Mr. Powell’s successor much earlier than typically is the case in a bid to further undermine the chair.

Trying to fire Mr. Powell would be a major escalation in the administration’s campaign against the Fed chair, who has so far rebuffed Mr. Trump’s demands to significantly lower interest rates. Mr. Powell’s term as chair officially ends in May, but is able to stay on as a member of the Board of Governors until 2028 if he chooses to.

Presidents are unable to remove officials at the Fed without cause, a protection that was bolstered by the Supreme Court in a ruling in May regarding Mr. Trump’s ability to unseat certain members of government agencies stipulated as independent by Congress.

Cause has typically meant malfeasance or gross misconduct, rather than a disagreement on the direction of monetary policy. No president has attempted to fire a Fed chair in modern history.

Investors have become used to Mr. Trump’s threats in recent months, and markets have tended not to react strongly to his social media posts attacking Mr. Powell. But that could change if investors begin to think the president will actually go through with his threats.

Markets have generally assumed that Mr. Trump is merely “playing chicken,” said Tara Sinclair, an economist at George Washington University, who studies the Fed. But the closer Mr. Trump comes, the greater the risk that he actually follows through.

“It starts to become, ‘Wait, are you actually going to do this?’” Ms. Sinclair said. That could have serious economic consequences, she added.

— Benjamin Casselman, Tony Romm and Erica Green contributed reporting.