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 has reportedly weighed replacing 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 after the November midterm elections.

White House aides told The New York Times for a story published Saturday that Trump has mulled tapping a new Pentagon chief who would be more like Secretary of State Mike Pompeo Michael (Mike) Richard PompeoTreasury sanctions individuals, groups tied to Russian malign influence activities Navalny released from hospital after suspected poisoning Overnight Defense: Pentagon redirects pandemic funding to defense contractors | US planning for full Afghanistan withdrawal by May | Anti-Trump GOP group puts ads in military papers MORE in being a vocal supporter of his policies.

Trump and Mattis have reportedly butted heads over a number of policy issues, such as banning transgender people from serving in the military, military exercises with South Korea and the United States's posture toward NATO.

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The Times, citing multiple current and former officials, reported that Trump chafes at comparisons with Mattis that cast the former Marine as the adult in the room.

Aides also told the Times that Mattis has grown weary of beating back requests from Trump that he disagrees with while taking great pains to appear publicly loyal to the president.

“Secretary Mattis is probably one of the most qualified individuals to hold that job,” Sen. Jack Reed John (Jack) Francis ReedWhen 'Buy American' and common sense collide Hillicon Valley: Russia 'amplifying' concerns around mail-in voting to undermine election | Facebook and Twitter take steps to limit Trump remarks on voting | Facebook to block political ads ahead of election Top Democrats press Trump to sanction Russian individuals over 2020 election interference efforts MORE (D-R.I.), the ranking member of the Senate Armed Services Committee, told the Times.

Reed said a Mattis departure from the Pentagon “would, first of all, create a disruption in an area where there has been competence and continuity.”

However, Trump reportedly took exception to an anecdote in veteran journalist Bob Woodward’s book in which Mattis likened the president’s intellect to that of a “fifth or sixth grader.” Mattis has called Woodward's reporting on him "fiction."

But that anecdote, combined with other stories in the book and a Times op-ed that skewers the president authored by an anonymous senior administration official, have the president wondering if the walls are closing in on him and needs more of a loyalist in the Pentagon, the newspaper reported.

Associates of Mattis told the Times it is highly unlikely the Defense chief would abandon his apolitical view in leading the Department of Defense.