The disclosure that Ronna McDaniel is planning to step down this month as the leader of the Republican National Committee has set off a new round of jockeying between two of the same men who battled for the co-chairman post last year.

As he did last year, Donald J. Trump, the Republican front-runner for the White House, looks likely to back Michael Whatley, an election-denying ally — this time, though, as Ms. McDaniel’s replacement.

But Mr. Whatley, the chairman of the North Carolina Republican Party, was not successful last year. And while the former president wields broad influence over who leads the party, his power is not absolute. And Republican committee members may not be in lock step.

“It looks like a fight is breaking out for chair with conservatives lobbying for Drew McKissick (SC) to take over as interim chair,” Tyler Bowyer, a committee member from Arizona, wrote on X on Tuesday night.

It was Mr. McKissick who prevailed in the co-chairman contest last year, when Mr. Whatley, who was trailing in the vote, withdrew from the contest after the second ballot. Under the party’s rules, Mr. McKissick would become the committee’s interim chairman after Ms. McDaniel steps down and until her replacement is elected by the committee.

Mr. McKissick, the chairman of the South Carolina Republican Party, has in recent days expressed his appetite for the job directly to Mr. Trump, several people familiar with the situation said.