Arkansas Republican Sen. Tom Cotton would move into Pompeo’s position, the news outlet said citing senior administration officials.
White House Chief of Staff John Kelley reportedly developed the plan, which is said to be scheduled around the year’s end.
Trump did not dispute the report that White House officials are readying a plan to replace Tillerson send Cotton to lead the CIA.
“He’s here. Rex is here,” Trump told pool reporters Thursday.
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White House Press Secretary Sarah Huckabee Sanders tried to tamp down the Times report, but like the president she did not call the report false.
“As the President just said, ‘Rex is here.’ There are no personnel announcements at this time,” Sanders said in a statement. “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.”