WASHINGTON — The White House has developed a plan to force out Secretary of State Rex W. Tillerson, whose relationship with President Trump has been strained, and replace him with Mike Pompeo, the C.I.A. director, perhaps within the next several weeks, senior administration officials said on Thursday.

Mr. Pompeo would probably be succeeded at the C.I.A. by Senator Tom Cotton, a Republican from Arkansas and key ally of the president on national security matters, according to the White House plan. Mr. Cotton has signaled that he would accept the job if offered, said the officials, who insisted on anonymity to discuss sensitive deliberations before decisions are announced.

Mr. Trump has not signed off on the plan developed by John F. Kelly, the White House chief of staff, officials said, but the president is said to have soured on Mr. Tillerson and is ready to make a change at the State Department. Mr. Trump spoke harshly about Mr. Tillerson in front of White House aides as recently as Thursday but did not seem ready yet to replace him, according to one person close to the president.

For all his public combativeness and his “you’re fired” reputation from reality television, Mr. Trump is often reluctant to dismiss advisers. The disclosure of Mr. Kelly’s transition plan may have been a way to nudge him into making a decision, according to that person. It may also have been meant as a not-too-subtle message to Mr. Tillerson that it is time to go.