The White House is discussing plans to replace Secretary of State Rex Tillerson with CIA chief Mike Pompeo, US media say.
Mr Tillerson has been at odds with Mr 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.
Two White House officials were quoted by Associated Press as saying a plan was being discussed, and unnamed government sources also spoke to the New York Times and Vanity Fair.
Mr 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 Mr Trump has given final approval to the move, the NYT reports.
Mr Trump’s disenchantment with Mr Tillerson, a former chief executive of energy giant Exxon Mobil, has been rumoured for some time.
The secretary of state has defended the multi-party deal to curb Iran’s nuclear ambitions in return for a loosening of sanctions – an agreement derided by Mr Trump.
The president also said in October that Mr Tillerson was “wasting his time” trying to bring about diplomatic contacts with North Korea as it continues to build up its missile and nuclear capabilities.
The secretary of state’s firing would form part of a wider national security team shake-up overseen by White House Chief of Staff John Kelly, the NYT reports.
Mr Tillerson, 65, was appointed in January and his replacement would cap one of the shortest tenures for an American secretary of state.
His appointment was a controversial one, thanks to his close links to Russian President Vladimir Putin stemming from his work on major oil contracts in Russia.
The Trump administration faces several investigations into whether there was collusion between his election campaign and Russian officials.
Mr Tillerson was on the verge of retirement when he was asked to fill the role.
Interviewed earlier this year by the conservative website, Independent Journal Review (IJR), he was quoted as saying: “I didn’t want this job. I didn’t seek this job …my wife told me I’m supposed to do this.”
The Texas native has embarked on radical plans to “create the state department of the future”, involving the sacking of career diplomats and budget cuts.
Democrats, and some Republicans, have expressed concern the restructuring could undermine America’s interests abroad.