President Trump Donald John TrumpFederal prosecutor speaks out, says Barr 'has brought shame' on Justice Dept. Former Pence aide: White House staffers discussed Trump refusing to leave office Progressive group buys domain name of Trump's No. 1 Supreme Court pick MORE has floated Treasury Secretary Steven Mnuchin Steven Terner MnuchinThe Hill's Morning Report - Sponsored by Facebook - Republicans lawmakers rebuke Trump on election On The Money: Anxious Democrats push for vote on COVID-19 aid | Pelosi, Mnuchin ready to restart talks | Weekly jobless claims increase | Senate treads close to shutdown deadline Vulnerable Democrats tell Pelosi COVID-19 compromise 'essential' MORE and White House counselor Kellyanne Conway Kellyanne Elizabeth ConwaySpecial counsel investigating DeVos for potential Hatch Act violation: report George and Kellyanne Conway honor Ginsburg Trump carries on with rally, unaware of Ginsburg's death MORE as possible replacements for acting White House chief of staff Mick Mulvaney Mick MulvaneyOn The Money: House panel pulls Powell into partisan battles | New York considers hiking taxes on the rich | Treasury: Trump's payroll tax deferral won't hurt Social Security Blockchain trade group names Mick Mulvaney to board Mick Mulvaney to start hedge fund MORE, Bloomberg News reported Tuesday.

Trump reportedly told Mnuchin about a month ago, “You have such great ideas. Why don’t you be my chief?” according to Bloomberg.

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People familiar with the matter told the news outlet that Trump has made similar remarks to deputy chief of staff Chris Liddell and has asked advisers if Conway would be a good choice for the position.

White House aides told Bloomberg that Trump’s comments about a possible replacement are not new, as he usually tests different considerations in conversations with aides.

The Hill has reached out to the White House and the Treasury Department for comment.

Mulvaney has come under intense scrutiny from the president’s allies after saying in a televised press conference last week that security aid to Ukraine was partly dependent on the country investigating a conspiracy theory undermining the conclusion that Russia interfered in the 2016 U.S. presidential election.

“I have news for everybody: Get over it,” Mulvaney said. “There's going to be political influence in foreign policy.”

The White House this week said Mulvaney has Trump's backing.

"Mick Mulvaney’s standing in the White House has not changed. He is still the Acting Chief of Staff and has the President’s confidence," deputy White House press secretary Judd Deere told The Hill in a statement Monday.