Rex Tillerson will remain as U.S. secretary of state, a White House spokesperson said on Thursday, amid reports Tillerson will be removed in favour of Mike Pompeo, who is currently CIA director.

"When the president loses confidence in someone, they will no longer serve here," White House press secretary Sarah Sanders said when asked about reports of a staff shakeup.

During repeated questions from reporters during the daily press briefing, Sanders didn't answer yes or no to whether Tillerson was on the way out, but pointed out two meetings between U.S. President Donald Trump and Tillerson on Thursday.

Trump himself was coy when asked by a reporter whether he wanted Tillerson on the job, pointing out that Tillerson was in the building.

"He's here. Rex is here," Trump said.

The reports circulating earlier in the day, also had Republican Sen. Tom Cotton being tapped to replace Pompeo at the CIA, the New York Times reported, citing senior officials.

The Times, the first to report the plan, said it was not immediately clear whether Trump had given final approval to the plan.

Tillerson was unaware of any plans to oust him when he spoke to Sen. Bob Corker on Thursday, Corker said.

"He's conducting business, as is the norm, and is unaware of anything changing," Corker, chairman of the U.S. Senate committee on foreign relations, told reporters.

Tillerson's departure would end a troubled tenure for the former ExxonMobil chief executive who has found himself increasingly at odds with Trump over policy challenges, such as North Korea and under fire for his planned cuts at the State Department.

John Kelly, the White House chief of staff, developed the transition plan and has discussed it with other officials, the Times reported. Under his plan, the staff reshuffle would happen around the end of the year or shortly afterward.

CIA director Mike Pompeo could wind up with Tillerson's job, the New York Times suggests. (Pablo Martinez Monsivais/Associated Press)

Tillerson's departure has been widely rumoured for months, with attention focused on Nikki Haley, U.S. ambassador to the United Nations, as his likely replacement.

But Pompeo, a former three-term member of Congress, has increasingly moved to the forefront as he gained Trump's trust on national security matters.