There has been growing concern among Trump and his allies that Mueller's past professional relationship with Comey is getting in the way of his investigation into Russia's interference of 2016 presidential election, IBT wrote.

Reports also said the president, at one point, thought of firing Mueller because he thought the special counsel was a part "witch hunt" against him. However, Trump's top aides talked him out of taking any extreme step, which they believed, would harm the administration.

Read alsoPence hires outside legal counsel – Washington PostNow, Richard W. Painter, the former White House ethics lawyer tweeted Saturday saying: "Just appeared on FOX News. They are building a case for firing Mueller. If that happens Mike Pence will soon become the 46th President."

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"Mueller is absolutely not compromised by his professional relationship with Comey," Painter said, according to the Hill. "This is just an effort to undermine the credibility of the special counsel."

According to a Washington Post report Wednesday, Mueller was investigating the president for obstruction of justice and was interviewing Director of National Intelligence Dan Coats, National Security Agency Director Mike Rogers and Richard Ledgett, the recently retired deputy NSA director.

Read alsoComey: Trump administration 'lied' about the FBI – BBCMueller's move came after Comey said in his June 8 testimony to the Senate Intelligence Committee that he intentionally handed over his memos, detailing each conversation he had with the president, over to Mueller. Both Comey and Mueller know each other for 15 years and the former FBI director gave the memos to the latter because he knew Mueller would launch a probe into whether Trump obstructed justice by urging Comey to end investigation into former National Security Advisor Michael Flynn's connections to Russia.

"I don't think it's for me to say whether the conversation I had with the President was an effort to obstruct," Comey said in his testimony. "I took it as a very disturbing thing, very concerning, but that's a conclusion I'm sure the special counsel will work towards, to try and understand what the intention was there, and whether that's an offense," he added.

In May, Deputy Attorney General Rod Rosenstein appointed Mueller as special counsel to lead the probe. The appointment was welcomed by both Democrats and Republicans. However, in recent days, the special counsel came under the radar of Trump and allies over his friendship with Comey. They also argued Mueller's decision to hire prosecutors who have donated to Democratic candidates indicated there was conflict of interests between the special counsel and the president.

On Thursday, Trump appeared to criticize Mueller on Twitter saying the Russia investigation being "led by some very bad and conflicted people."