Washington (CNN) The White House is contemplating a scenario to replace Secretary of State Rex Tillerson with CIA Director Mike Pompeo within the next few months, multiple government officials tell CNN.

The vacancy at the CIA would likely be filled, according to the tentative plan, by Sen. Tom Cotton, a hawkish Arkansas Republican, the sources said.

There's no decision yet on the timing of Tillerson's departure, which has been expected for months. But multiple sources close to the White House and across government said Pompeo is the leading candidate to take over at the State Department.

President Donald Trump offered, "He's here, Rex is here," when asked if he wants Tillerson to stay on the job by reporters at the White House Thursday after the news broke of the potential exit plan.

"As the President just said, 'Rex is here,' " White House press secretary Sarah Sanders said in a statement, adding that the administration has no personnel announcements to make.

"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," she said.

The New York Times reported Thursday morning that the plan to replace Tillerson has been developed by White House chief of staff John Kelly and is likely to be triggered late this year or early next year.

The news fleshes out some detail on a possible Tillerson ouster, anticipated for months as tensions between the top US diplomat and Trump have played out in unprecedented public fashion. Accounts of Tillerson dismissing the President as a "moron" have been matched by Trump's public statements deriding Tillerson for "wasting his time" on diplomatic efforts.

The tepid expressions of support that regularly followed these reports haven't been enough to dampen speculation, as support for Tillerson has eroded across Washington in the nearly 10 months since his appointment.

Administration officials have chafed at Tillerson's resistance to Trump policy positions, lawmakers have expressed alarm about his cuts to the State Department, staff there decry the agency's dysfunction and senior members of the US national security establishment from both parties warn that he is creating a "national security emergency," in the words of former Secretary of State Madeleine Albright.

When, not if

For weeks, Tillerson's departure has been a "when, not if" question in Washington. It's a secret so open that in October Pompeo and a staff member openly discussed when the CIA director would move to the State Department, a person present in the room told CNN.

The switch at the top levels of the Trump administration's national security team would come at a time of bristling tension with nuclear armed North Korea, which now has the capability to reach the US with its missiles. That's one reason the news about Tillerson provoked dismay in some quarters and an accusation of skullduggery.

"It's been evident to me that for some time, somebody is seeking to undermine his presence here," said Sen. Bob Corker, the Tennessee Republican who chairs the Senate Foreign Relations Committee. "

I don't know who that is," said Corker, who has long argued that the US needs Tillerson in place as a stabilizing presence on the administration's national security team.

"We and the rest of the world need someone like Tillerson in that position," Corker said. "Especially when the world's on fire ... Rex Tillerson is a strategic thinker."

Defense Secretary James Mattis said Thursday that "there's nothing to" the rumors about Tillerson being forced out by the White House.

"I make nothing of it, there's nothing to it," Mattis said before a bilateral meeting with Libya's Prime Minister.

The expected shake-up would take the role of top US diplomat out of the hands of an official whose relationship with the President has grown increasingly fractured and put it into the hands of another whose bond with Trump has only strengthened this year.

Pompeo, a former Republican congressman from Kansas, has grown increasingly close to the President in recent months -- a bond largely formed over the President's free-wheeling daily intelligence briefings, which one White House official said Pompeo delivers in person three to four times a week.

After the briefings, Trump frequently asks Pompeo -- who graduated first in his class at the US Military Academy at West Point and went on to Harvard Law School -- to stick around to continue chatting one-on-one, the official said.

A source close to Pompeo says the President hasn't told the director about the plan in any certain terms, but there has been a quiet sense in Pompeo world that this is certainly possible, perhaps even likely. They caution that the decision is obviously Trump's call and they are well aware that someone's standing with the President can change at any time.

Pompeo would accept this elevation without hesitation, this source says.

Publicly undercut

Since he was sworn into office on February 1, Tillerson had to contend with a President who publicly undercut him, a shadow State Department that sprang up under Trump's son-in-law Jared Kushner, competition from US Ambassador to the UN Nikki Haley, and a litany of complaints from diplomats, foreign ministers and others in Washington that his State Department was deeply dysfunctional.

Tillerson aggressively pushed back against those claims in a November 28 appearance, portraying it as an insult to State Department staff.

"I'm offended on their behalf when people say somehow we don't have a State Department that functions," Tillerson said. "I can tell you it's functioning very well from my perspective."

But a steady drip of negative news, and reports of Tillerson's alleged resentment over Ivanka Trump leading a delegation to the Global Entrepreneurship Summit in India, in November, continued to undermine the former ExxonMobil CEO.

The painfully public airing of his troubles with the President perhaps hit a low when one lawmaker faulted Trump for his tendency to "publicly castrate" the secretary of state. That exchange forced Tillerson, when asked about the comment by CNN's Jake Tapper, to declare: "I checked. I'm fully intact."

Corker had told the Washington Post that Trump repeatedly neutered Tillerson with Tweets that undermined or flatly contradicted policies he was pursuing. That, Corker said, shut down options for the US and damaged Tillerson's efforts to peacefully resolve tensions with North Korea.

The castration episode followed an extraordinary October 4 public statement in which Tillerson stressed his commitment to his job as secretary of state, but didn't definitively deny an NBC report that he had called Trump a "moron."

That report also detailed Tillerson's "fury" about the ways Trump has undermined him publicly on several foreign policy initiatives and his thoughts about resigning.

Calling the story "erroneous" during his remarks, Tillerson pointed the finger at "some who try to sow dissension" to undermine the President's agenda and said he has been asked "repeatedly" if he's going to step down.

"For some reason, it continues to be misreported," Tillerson said. "There's never been a consideration in my mind."

Soon after that, in mid-October, an administration official was telling CNN that Tillerson was on thin ice, even as the President was publicly declaring he had confidence in his top diplomat.

"It certainly isn't a good relationship, and its problems that have been building," the official said of Tillerson's fate in the Trump administration. "I think everyone is trying to stick it out for a variety of selfish reasons. But not for the same reasons."