Mnuchin tweeted late on Saturday that Trump told him he never suggested dismissing the Fed chief, a move that could roil the already volatile financial markets, sources familiar with the situation had said.
"I never suggested firing Chairman Jay Powell, nor do I believe I have the right to do so," Mnuchin quoted Trump as telling him.
Earlier source-based reports on Saturday had in the US media talked about the Trump decision to fire Powell, CNBC said.
However, later in the day, other sources said that they did not expect the President to dismiss the US central bank chief despite his public and private objections to the Fed's interest rate-hiking campaign and repeated criticism of Powell, whom he appointed, the CNBC reported.
The Fed has declined to comment when asked about the latest development.
In an email to CNBC, Greg Valliere, chief global strategist at Horizon Investments, lambasted the idea as "insane" and "utter madness."
In response to an inquiry, White House Press Secretary Sarah Huckabee-Sanders said: "I'm aware of no plans to fire Powell."
An attempt to remove the Fed chairman would be unprecedented and seen as an attack on the US central bank's independence. It would be on potentially shaky legal ground, and would probably hit financial markets around the globe, the CNBC reported.
Trump has frequently attacked Powell, who was sworn in as Fed chairman in February 2017, and the Fed for raising borrowing costs recently, especially as US stocks have tumbled and yields on US government debt have begun to signal a possible recession ahead.
Before the central bank's policy meeting earlier this week, Trump, a former business tycoon, had warned against lifting rates when stock markets were slumping.
Despite the public jaw-boning, the central bank lifted rates for the fourth time this year on Wednesday, citing the US economy's continued strong performance.
US stocks and bond yields fell hard after the decision. The Dow Jones industrial average had its worst week since the 2008 financial crisis, while the Nasdaq sank into bear market territory.
Earlier in December, Trump, in an interview, had said he liked Powell, but not his policies.
"I think he's a good man. I think he's trying to do what he thinks is best. I disagree with him," Trump said. "I think he's being too aggressive, far too aggressive, actually far too aggressive."