WASHINGTON — President Trump is expected to name Gen. Mark A. Milley, the Army chief of staff, to be the next chairman of the Joint Chiefs of Staff, the top-ranking military position in the country, administration officials said on Friday.

Mr. Trump teased the decision in remarks to reporters at the White House on Friday, saying that he would make an announcement at the Army-Navy football game on Saturday in Philadelphia.

“I can give you a little hint: It will have to do with the Joint Chiefs of Staff and succession,” the president said.

Mr. Trump, who made several staff change announcements on Friday, met two weeks ago with General Milley and the Air Force chief of staff, Gen. David L. Goldfein, the two men believed to be in contention to succeed Gen. Joseph F. Dunford Jr. of the Marines, whose term as chairman expires next autumn.