The chairwoman of the Republican National Committee, Ronna McDaniel, has told former President Donald J. Trump she is planning to step down shortly after the South Carolina primary on Feb. 24, according to two people familiar with the plans.

Mr. Trump is then likely to promote the chairman of the North Carolina Republican Party, Michael Whatley, as her replacement, according to several people familiar with the discussions. Under the arcana of the committee’s rules, however, Mr. Trump cannot simply install someone. A new election must take place, and Mr. Whatley could face internal party dissent.

Ms. McDaniel has faced months of pressure, a campaign from Trump-allied forces to unseat her and growing dissatisfaction and anxiety in the Trump camp about the strained finances of the R.N.C. as the general election cycle begins early.