President Trump Donald John TrumpOmar fires back at Trump over rally remarks: 'This is my country' Pelosi: Trump hurrying to fill SCOTUS seat so he can repeal ObamaCare Trump mocks Biden appearance, mask use ahead of first debate MORE is being cautioned by top advisers to not back a candidate in the race to replace retiring Speaker Paul Ryan Paul Davis RyanKenosha will be a good bellwether in 2020 At indoor rally, Pence says election runs through Wisconsin Juan Williams: Breaking down the debates MORE (R-Wis.), ABC News reported.

Trump reportedly wanted to endorse House Majority Leader Kevin McCarthy Kevin Owen McCarthyMcCarthy's Democratic challenger to launch first TV ad highlighting Air Force service as single mother Trump asked Chamber of Commerce to reconsider Democratic endorsements: report The Hill's Morning Report - Sponsored by The Air Line Pilots Association - White House moves closer to Pelosi on virus relief bill MORE (R-Calif.), but was asked to hold off from backing a lawmaker to replace Ryan.

Vice President Pence 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 are among those cautioning Trump to stay out of the race, fearing it could complicate the competition and the president’s relationship with the winner, according to ABC.

Trump and McCarthy, who have had a close relationship, reportedly discussed the lawmaker becoming Speaker at a White House dinner with Republican leadership last week, according to The Associated Press.

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Ryan, who announced his retirement last week, has backed McCarthy as his replacement.

However, House Majority Whip Steve Scalise Stephen (Steve) Joseph ScaliseHouse GOP slated to unveil agenda ahead of election House panel details 'serious' concerns around Florida, Georgia, Texas, Wisconsin elections Scalise hit with ethics complaint over doctored Barkan video MORE (R-La.) is also considered a front-runner for the job.

Scalise said after Ryan’s endorsement that he wouldn't run against McCarthy.

Rep. Jim Jordan James (Jim) Daniel JordanSunday shows preview: Justice Ginsburg dies, sparking partisan battle over vacancy before election House passes resolution condemning anti-Asian discrimination relating to coronavirus Republicans call for Judiciary hearing into unrest in cities run by Democrats MORE (R-Ohio), a founding member of the conservative House Freedom Caucus, is also considering running for Speaker.