President Trump Donald John TrumpBiden on Trump's refusal to commit to peaceful transfer of power: 'What country are we in?' Romney: 'Unthinkable and unacceptable' to not commit to peaceful transition of power Two Louisville police officers shot amid Breonna Taylor grand jury protests MORE is frustrated with Defense Secretary James Mattis James Norman MattisBiden courts veterans amid fallout from Trump military controversies Trump says he wanted to take out Syria's Assad but Mattis opposed it Gary Cohn: 'I haven't made up my mind' on vote for president in November MORE and has privately disparaged the retired Marine general as a moderate unwilling to bend to Trump's policy positions, according to a new report.

Politico reports that the president has privately coined a new nickname for him, "Moderate-Dog Mattis," a riff off of Mattis's famous "Mad Dog" moniker.

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Trump has begun using the nickname behind closed doors, even as Mattis remains in the administration, Politico reports.

Administration officials tell the news outlet that they expect Mattis to resign or be dismissed following November's midterm elections. But Trump's allies in the GOP-held Senate tell Politico that they are not eager to see Mattis leave.

“He does a great job,” Sen. John Barrasso John Anthony BarrassoThe conservative case for phasing out hydrofluorocarbons GOP senator attacks Biden: 'I'm not sure what he recalls' Oil and gas is a partner — not an adversary — in meeting our economic and environmental goals MORE (R-Wyo.) told Politico, adding that Mattis should "absolutely" stay on.

Sen. James Inhofe James (Jim) Mountain InhofeChamber of Commerce endorses McSally for reelection Overnight Defense: Top admiral says 'no condition' where US should conduct nuclear test 'at this time' | Intelligence chief says Congress will get some in-person election security briefings Top admiral: 'No condition' where US should conduct nuclear test 'at this time' MORE (R-Okla.), the newly selected head of the Senate Armed Forces Committee, added that whether or not Mattis is replaced could “depend on whether I have anything or not to say about it.”

News of Mattis's possible exit from the administration comes amid the release of journalist Bob Woodward's new book, "Fear: Inside the Trump White House," in which Mattis is quoted as disparaging Trump's understanding of the Korean Peninsula as that of "a fifth- or sixth-grader."

Mattis fired back in a statement following the book's release, writing that "the contemptuous words about the President attributed to me in Woodward's book were never uttered by me or in my presence."

Woodward, however, contends that Mattis and White House chief of staff John Kelly John Francis KellyMORE, also a retired Marine general, are lying in their denials about comments attributed to them in the book.

“They are not telling the truth," Woodward told NBC News. “These people, these are political statements to protect their jobs, totally understandable."

The president claimed Wednesday that both Mattis and Kelly were "insulted" by the reporting in Woodward's book, which was released Tuesday to heavy media attention.

“[Mattis] was insulted by the remarks that were attributed to him and he came out with a very strong statement. I assume you read it, I hope you read it last night," Trump said.

"Gen. John Kelly, the same exact thing. He said he was insulted by what it said. He's right here. He's insulted by it, he couldn't believe what they said, and he put out a very strong statement,” Trump added.