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, within the next several weeks, senior administration officials said on Thursday.

Mr. Pompeo would be replaced at the C.I.A. by Senator Tom Cotton, a Republican from Arkansas who has been a 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.

It was not immediately clear whether Mr. Trump has given final approval to the plan, but he has been said to have soured on Mr. Tillerson and in general is ready to make a change at the State Department.