Mr Comey said he was "sure" Mr Mueller was looking at whether Mr Trump had obstructed justice, but added that to his knowledge, the president had not tried to impede the Russian Federation inquiry.
The president complained the probe is unfair and wondered why his defeated Democratic opponent wasn't getting the same scrutiny.
Mr Comey, who had been leading one of several Russian Federation inquiries, testified to Congress last week that the president had pressured him to drop an inquiry into links between Mr Flynn and Russian Federation.
"I believe so", she said, but added that she had not spoken to Trump about it.
ABC News reported on Friday that Rosenstein has privately said he may need to recuse himself from matters relating to the Russian Federation probe, given that he could become a potential witness in the investigation.
Speaking to reporters during an off-camera, unrecorded briefing, Sanders said Trump "has the right to" fire Mueller as special counsel but "has no intention to do so". Should he become a witness, he would certainly have to recuse, which means that he'd be replaced with the DOJ's third in command, Associate Attorney General Rachel Brand.
Trump may be referring to Deputy Attorney General Rod Rosenstein, who in a memo to Trump raised concerns over Comey's performance.
Comey's accounts of his conversations with Trump, which the president has vociferously denied, could serve as key evidence if Mueller moves forward with an obstruction case.
Moscow has denied USA intelligence agencies' conclusion that it interfered in last year's election campaign to try to tilt the vote in Trump's favour. By tweeting that he is under investigation, Trump essentially confirmed Wednesday's Washington Post story which broke the news by leaning on anonymous sources close to the investigation.
The White House has directed questions for details to outside legal counsel, which has not responded.
The president tweeted Friday, "After 7 months of investigations & committee hearings about my 'collusion with the Russians, ' nobody has been able to show any proof. Sad!" he wrote in one post.
The Post reports the other members include: 'former national security adviser Michael Flynn, former campaign chairman Paul Manafort and Carter Page, who was listed as a foreign-policy adviser for the campaign'. Pence's office confirmed he had retained Richard Cullen, a former Virginia attorney general and US attorney for the Eastern District of Virginia, to assist "in responding to inquiries" from Mueller. Now, according to The Washington Post, special counsel Robert Mueller is also looking into the Kushner's business dealings.
Examining such possible charges will allow investigators to interview key administration figures including Attorney General Jeff Sessions, Rosenstein and possibly Trump himself, the source told Reuters.