Kelly is expected to be replaced with Nick Ayers, who is now chief of staff to Vice President Mike Pence.
Sources tell CNN that "Kelly responded to a narrow set of questions from special counsel investigators after White House lawyers initially objected to Mueller's request to do the interview earlier this summer".
The special counsel's team questioned Kelly specifically on an episode involving Trump after the New York Times reported that a year ago Trump sought to fire Mueller - a report that allegedly drew Trump's ire at then-White House counsel Don McGahn, who didn't publicly deny it. CNN, citing its sources, said their relationship was now worse than ever and that the two were not on speaking terms, but added that no decision on Kelly's possible departure was final until it was announced.
But the story line of Kelly's departure has been protracted for so many months that White House aides often now just shrug.
Mike Pence's chief of staff Nick Ayers has reportedly been angling for the job and is seen as the leading candidate.
Kelly, a retired general and the former secretary of the Department of Homeland Security, has been chief of staff since July 2017.
The president began Friday by attacking the soon-to-be published report by special counsel Robert Mueller.
Kelly, a decorated Marine Corps general, is widely regarded as one of the most well-respected and qualified members of the Trump administration. But as of an hour ago, he hadn't been fired or resigned. Lights are off in Kelly's office this morning, per a senior admin official.
Kelly is the latest high-ranking White House official known to have given information for Mueller's probe.