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.
Yet as Mr. Trump marches toward securing the G.O.P. nomination, it is Mr. Whatley who is widely viewed as the heir apparent to Ms. McDaniel, according to several people familiar with the discussions.
“The nominee gets his way,” said Ed Broyhill, a committee member from Mr. Whatley’s state of North Carolina.
But Mr. McKissick has his fans.
“Certainly, he would be a top choice of mine,” Oscar Brock, a committee member from Tennessee, said on Wednesday. Mr. Brock, who opposed Ms. McDaniel’s re-election as the committee’s chairwoman last year, said Mr. McKissick’s interest in the post was apparent when the two spoke on Tuesday.