(CNN) President Donald Trump denied on Friday that he had moved to fire special counsel Robert Mueller.

He had called for the firing last June, according to one person familiar with the matter. White House counsel Don McGahn refused to order the Justice Department to fire Mueller because he disagreed with the President's reasoning, the source said. However, according to the source, McGahn did not threaten to resign directly to the President.

"Fake news, folks. Fake news," Trump said when questioned about the revelation as he entered the World Economic Forum in Davos.

"Typical New York Times," he added.

The timing at issue last summer was just a month after Trump fired former FBI Director James Comey in May. Later that month, Mueller was appointed by the Department of Justice to manage the special counsel investigation into possible Russian meddling in the 2016 election.

In June, The Washington Post reported that Mueller's investigation was broadening to include looking into a potential obstruction of justice case.

White House lawyer Ty Cobb declined to comment on the President's actions to CNN, citing "respect for the Office of the Special Counsel and its process."

Two people told the Times that Trump expressed concern over three possible conflicts of interest, including a dispute Mueller had involving Trump National Golf Club, the law firm Mueller previously had worked at and the fact that Mueller had recently been interviewed to head the FBI.

The Times said the discussion over Mueller's potential conflicts of interest in June 2017 arose following reports that Mueller was looking into a possible obstruction of justice case.

Mueller is currently investigating any possible ties between the Trump campaign and Russia during the 2016 US election. Trump has repeatedly denied any collusion between his campaign and Russia.

The White House has repeatedly denied that Trump was looking at firing the special counsel. In August, White House lawyer John Dowd told USA Today the idea had "never been on the table."

"That's never been on the table, never,'' Dowd said of firing Mueller, according to USA Today's August story. "It's a manifestation of the media. My dealings with Bob Mueller have always been cordial, respectful -- the way it should be."

Reacting to The New York Times' story. Sen. Mark Warner, the ranking Democrat on the Senate Intelligence Committee, said, "Firing the special counsel is a red line that the President cannot cross."

In a statement, the Virginia Democrat added, "Any attempt to remove the special counsel, pardon key witnesses, or otherwise interfere in the investigation, would be a gross abuse of power, and all members of Congress, from both parties, have a responsibility to our Constitution and to our country to make that clear immediately."

Former White House Communications Director Anthony Scaramucci dismissed the report while on CNN on Thursday evening.

Scaramucci told CNN's Chris Cuomo that The Times report is "totally irrelevant because he actually didn't fire Mueller."

Mueller's is just one of several ongoing investigations into Russian meddling in the 2016 US presidential election.

CNN confirmed Tuesday that both former FBI Director James Comey and Attorney General Jeff Sessions had been interviewed by the special counsel's team.

On Wednesday , Trump said he wants to speak with Mueller.

"I am looking forward to it, actually," Trump said, when asked if he was going to talk to Mueller. "Here is the story: There has been no collusion whatsoever. There is no obstruction whatsoever. And I am looking forward to it."

And later, he told reporters that he would do so under oath.

"I would do it under oath. I would do it," he said, later adding, "I would do it under oath, yeah."

Later Wednesday, Cobb responded to Trump's comments: "While Mr. Trump was speaking hurriedly before departing for Davos, he remains committed to continued complete cooperation with the OSC and is looking forward to speaking with Mr. Mueller."

Cobb added that the arrangements are still being worked out between Mueller's team and the President's personal lawyers.