Washington CNN  — 

The White House denied reports Thursday that President Donald Trump is searching for a replacement for chief of staff John Kelly. But the President has been privately polling aides and outside advisers for months now on possible successors, while maintaining to Kelly that he is happy with the job he is doing.

“He said it is absolutely not true and that it is fake news,” deputy press secretary Lindsay Walters told reporters Thursday.

“I’ve also spoken to General Kelly, who said this was news to him,” Walters added. “So both individuals in question have said there is no truth to this article.”

The White House similarly dismissed reports of the imminent departure of then-national security adviser H.R. McMaster shortly before he left.

Several people are considered to be in the running to replace Kelly, sources familiar with the situation tell CNN, including Office of Management and Budget Director Mick Mulvaney and Vice President Mike Pence’s top aide Nick Ayers.

But it’s unclear how serious Trump, who changes his mind regularly, is about Mulvaney and Ayers. There is no obvious successor for Kelly, which is why many believe Trump has not replaced him yet.

There has been tension between Trump and Kelly for months now, with Kelly threatening to quit on multiple occasions. Trump is irritated by the strict system Kelly has imposed on him, which he believes conflicts with his freewheeling nature; Kelly has been horrified by Trump’s defiant outbursts.

Lately, Trump has fluctuated between venting about Kelly to certain aides while reassuring others that he is pleased with him. He went on a profanity-laced tirade against his chief of staff during one conversation with an ally in recent weeks, a source who heard the conversation told CNN, but the next day he was telling others what a good job Kelly was doing.

Though Kelly was once quite influential, he is widely seen by staffers as on a downward slide. He has been less engaged in West Wing decisions and less visible in the President’s day-to-day activities. Trump has begun working around Kelly on a number of fronts, including during some calls with foreign leaders, on certain policymaking decisions, and in executing some of the past month’s staffing changes, people familiar with the matter said.

Kelly traveled with the President to Wisconsin on Thursday. When Air Force One returned to Joint Base Andrews outside of Washington Thursday evening, he followed Trump down the steps of the presidential plane and on to Marine One for the brief flight to the White House, unlike his predecessor Reince Priebus, who was fired on a rain-soaked tarmac at Andrews last summer.

CNN’s Gloria Borger, Jim Acosta and Kevin Liptak contributed to this report.