WASHINGTON—The White House is facing the prospect of another round of senior departures in the coming weeks as President Donald Trump approaches his one-year anniversary in office, according to several administration officials.

Secretary of State Rex Tillerson, the former Exxon chief executive who has struggled to mesh with Mr. Trump during their first year in office, is the most likely to leave, according to White House officials.

Senior officials say there is a lengthy list of White House aides and cabinet members potentially on their way out, with the first anniversary of the administration in mid-January serving as a natural off-ramp.

“There will be significant turnover at the one-year mark,” one senior administration official said. Another added: “You’re going to see plenty of movement.”

White House press secretary Sarah Huckabee Sanders said Thursday, “there are no personnel announcements at this time.”