The Trump administration has been embroiled in an investigation into alleged Russian interference into the 2016 USA election.
A spokesman for Mueller's team declined to comment on Wednesday.
"I know I'm not under investigation", Trump told NBC's Lester Holt in a May 11 interview that came just two days after Trump had fired Comey over, according to the President, the FBI director's handling of the Russian Federation investigation. "I also recognize the gravity of the committee's current investigation and the need for the American people to be presented the facts, so that they might make their own judgments".
The effort to muddy the waters surrounding the investigation is coming amid growing White House concern that the probe could detract from the president's agenda for months or years to come.
No one but Mueller and his team know how the Russian Federation investigations will move forward, but one thing's for sure - it's going to take time, probably years.
The former Alabama senator also defended himself against accusations that he misrepresented himself during his confirmation hearing when he said he hadn't met with Russian officials during the campaign.
Mueller had cleared Comey to testify last week. A highly regarded Justice Department careerist, he tapped Mueller - infuriating Trump - after the White House tried to pin the Comey firing on him.
If Trump instructs Rosenstein to dump Mueller, it would evoke memories of 1973, when the two top Justice Department officials, Elliott Richardson and Bill Ruckelshaus, resigned rather than obey President Richard Nixon's order to fire Archibald Cox, the special prosecutor conducting the Watergate investigation. This would amount to an implicit admission that the Washington Post report is accurate. The Post suggests Mr Comey's "carefully worded comments" could mean the investigation into Mr Trump began soon after Mr Comey was sacked. After a day of speculation, White House spokeswoman Sarah Huckabee Sanders said, "While the president has the right to, he has no intention to do so".
Comey testified before the Senate intelligence committee last week and confirmed that he gave Mueller the memos he wrote detailing his interactions with Trump ahead of his firing.
"I think, frankly, our story shows that the president is by no means out of the woods as far as the investigation goes", the Post's Barrett told NPR. The two sides have been discussing "deconfliction" - or how the Senate investigation and the federal probe will share information and not step on each others' toes. Trump - while not under oath, it's worth noting - has insisted flatly that he had never urged Comey to slow or stop the Flynn investigation. The Justice Department has long held that it would not be appropriate to indict a sitting president.
"I'm going to acknowledge we had a meeting with the special counsel Mueller, but I'm not going to get into the contents", Mark Warner, the ranking Democrat on the Senate Intelligence Committee, told reporters later.
And he essentially warned Trump that if Mueller were to be fired, Rosenstein wouldn't be the one to do it, saying he saw no "good cause" to consider such a move. Comey said he told the president on three occasions that he wasn't personally under investigation.