The White House is discussing plans to replace Secretary of State Rex Tillerson with CIA chief Mike Pompeo, US media say.
Tillerson has been at odds with Trump over foreign policy recently.
The secretary of state was even reported to have privately described the president as a “moron”.
They have differed in their approach to North Korea’s missile testing and Iran’s nuclear programme, among other issues.
But the White House has said Tillerson continues in office; and the state department said “the rumours” were not true.
The reports emerged initially in the New York Times and Vanity Fair, quoting government sources.
Associated Press quotes two unnamed White House officials as saying a plan is being discussed.
Pompeo would be replaced at the CIA by Republican Senator Tom Cotton, the New York Times reports.
Reports suggest the change could take place as soon as December or in January.
However, it is not yet clear whether Trump has given final approval to the move, the NYT says.
“As the president just said: ‘Rex is here,” White House spokeswoman Sarah Sanders said in a statement.
“There are no personnel announcements at this time. Secretary Tillerson continues to lead the state department and the entire cabinet is focused on completing this incredibly successful first year of President Trump’s administration.”
Briefing reporters later, state department spokeswoman Heather Nauert admitted that Tillerson and Trump have had policy differences, but she said that Chief of Staff John Kelly had phoned the department to say “the rumours are not true.”
When asked how Tillerson, who is due in Europe next week, could continue to do his job while the White House was briefing he was about to lose it, she said: “The secretary of state is someone who doesn’t let his feathers get ruffled very easily.”
In further reaction to the reports, Senate Foreign Relations Committee Chairman Bob Corker said Tillerson was “unaware of anything changing”.