But others argued that any new secretary of state would face the same obstacles as Tillerson, who was undercut this year when Trump told his chief diplomat to stop "wasting his time" trying to negotiate with North Korea.
The ouster of Mr. Tillerson would end a turbulent reign at the State Department for the former Exxon Mobil chief executive, who has been largely marginalized over the past year.
In October, Tillerson shot down a report that said he had been on the verge of resigning from his Cabinet position over the summer.More news: Raiders' Michael Crabtree, Broncos' Aqib Talib ejected after fight
Asked whether he wanted Tillerson to remain in his job, Trump sidestepped the question, telling reporters at the White House: "He's here".
Tillerson answered that "the president speaks for himself".
If Trump went with Pompeo, he would tap a former Army armor officer and Harvard Law School graduate who was in his fourth term representing a Kansas district in Congress when he was chosen to lead the Central Intelligence Agency, where officials say he has enjoyed a less hostile relationship with career spies than Tillerson has had with career diplomats. She says Tillerson continues to lead the department. Axios's Mike Allen and Jonathan Swan reported last month that Pompeo's stock was rising in the White House and that he was a leading contender to replace Tillerson.
But he still would suffer from problems that have afflicted Tillerson, chief among them a boss who has shown little regard for diplomacy and no qualms about undermining his secretary of state with tweets, current and former USA officials said. Mr. Trump and Mr. Tillerson have been at odds over a host of major issues, including the Iran nuclear deal, the confrontation with North Korea and a clash between Arab allies.More news: Did you feel the DE quake ? (LIVE MAP)
If carried out, the staff changes would be the latest in a string of firings or resignations in the Trump administration including the departures of the chief of staff, national security adviser and Federal Bureau of Investigation director.
A source familiar with Tillerson's thinking said the secretary of state's original plan when he took the job was to leave in February.
More junior-level advisers could also use the completion of Trump's first year and tax legislation as a pivot point to move on, leading to another period of uncertainty that has at times overshadowed Trump's tenure, which began on January 20.More news: Fowl play: Trump officially pardons Drumstick the turkey