McGahn refused and said he would resign before carrying out the directive. "It reminds me, John, of the stated purpose of getting rid of [former FBI director] Jim Comey ... because he so mishandled the Hillary Clinton email investigation".
Mueller's is just one of several ongoing investigations into Russian meddling in the 2016 US presidential election.
McGahn also rarely travels with Trump or appears in public, with the exception of a speech he delivered at the Federalist Society in November. "And our sources, and I've checked in with many of them, they're not confirming that tonight".
Asked if he thought Mueller would be fair, he replied: "We are going to find out..."
Mueller has a sizeable budget and an open-ended term.
The episode has come to the attention of Mueller as he interviews various White House officials during the probe into whether Trump obstructed justice in the Russia inquiry, according to The New York Times. He has the power to prosecute federal crimes.
As more developments became public about the progress of the special counsel probe, Trump said Wednesday that he is "looking forward" to speaking with the special counsel. First, Trump said Mueller resigned from one of his golf clubs in an alleged dispute over fees. The Virginia senator has repeatedly criticized Trump for being "unwilling" to recognize the security threat posed by Russia.
Trump believed Mueller had three conflicts of interest that would have made it OK to fire him over.
Schiff said it would create chaos in Washington, D.C. if Trump were to oust Mueller: "Congress must make clear that any effort to remove the special counsel or impede his work would touch off a constitutional crisis, which would imperil this presidency and do grave damage to our nation". Mark Warner, the ranking Democrat on the Senate Intelligence Committee, said, "Firing the special counsel is a red line that the President cannot cross". Comey said he evaded those demands and was soon fired.
Trump pushed back against the report, without addressing the specific allegation, as he arrived Friday at the site of the World Economic Forum in Davos, Switzerland.
In the past week, some Republicans also cast doubt on the integrity of the investigation.