One source explained that Kelly, who is the biggest White House player to meet with the special counsel, had "ground rules" established by White House Counsel Emmet Flood for the interview. McGahn had refused to publicly deny the reporting.
Trump has engaged in talks with Nick Ayers, the vice president's chief of staff, about taking over the position, advisers said.
Trump had earlier pledged publicly that Kelly would remain through his first term in office, though many in the West Wing were skeptical.
Compounding the rumors were reports surrounding Kelly taking the day off on Friday, as the president traveled to Missouri.
The interview took place in recent months, the news network said, attributing the information to three people with knowledge of the matter. Kelly's shifting accounts caused his credibility inside the West Wing to plummet, and it never truly recovered, according to officials.
'Stranger Things' creators announce game based on the show
Before season 2, they collaborated on a Stranger Things mobile game that had a nice Legend of Zelda feel to it. Stranger Things 3: The Game should arrive sometime in 2019.
Kelly is the latest high-ranking White House official known to have given information for Mueller's probe.
Trump is further expected to announce Heather Nauert as the new USA ambassador to the United Nations on Friday, replacing Nikki Haley.
A source told Reuters last month that Trump was considering a replacement for Kelly. But this past summer, Kelly sought to quiet speculation that he was nearing the exit because of tensions with Trump by telling senior staff that he meant to remain as chief of staff through Trump's 2020 reelection campaign.
Barr, who also worked as AG for former President George HW Bush, replaces Jeff Sessions.
Trump had nothing but praise for the two new Cabinet members who he announced Friday he would nominate.
The president reportedly plans to make the announcement at Saturday's annual Army-Navy football game.