The talk about dismissing Mueller appeared to be coming from Trump allies - including some close to White House strategist Steve Bannon - who are increasingly frustrated with the prospect of a long and winding probe.
Ruddy said he spoke with Trump last week and he thought the president was "weighing" the option of firing Mueller judging by what the president's lawyers have been saying.
Press secretary Sean Spicer told NPR's Tamara Keith, "Mr".
The public testimony Tuesday before the Senate Intelligence committee should yield Sessions' most extensive comments to date on questions that have dogged his entire tenure as attorney general and that led him three months ago to step aside from the Russian Federation probe.
It should be noted Deputy Attorney General Rod Rosentein testified in front of the Senate Appropriations Committee Tuesday morning and said he is the only person who can remove Mueller from his position. "I don't think he's really pondering it", Rep. Adam Kinzinger said.
Trump does have the authority to remove the special counsel. He's bringing in some of the top prosecutors that have worked in the Justice Department.
Even as leading Republican legislators Tuesday waved off the idea of firing Mueller, expressions of discontent with Mueller have bubbled up nonetheless. Ruddy told PBS that he thinks it would be "a very significant mistake" for Trump to seek Mueller's termination. Doubt, however, has been cast on that explanation because of cryptic testimony from former FBI Director James Comey last week.
Asked whether he had seen any reason for Mueller to be removed, Rosenstein responded, "No, I have not". "One of my sources reached out to me just before we went on air, and they said there's mass hysteria in the West Wing about this". Trump surrogates like former House Speaker Newt Gingrich don't believe Trump would take such an explosive step.
Ann Coulter, a conservative activist tweeted that Attorney General Jeff Sessions never should've recused himself. The move came on the heels of word that Trump had asked Comey in February to jettison the bureau's investigation into Trump's former National Security Adviser Michael Flynn.
Rosenstein said he appointed Mueller and he stands by the decision. She said on Twitter: "Why do we need a special counsel now?"
Legal experts however say this would be incredibly hard, and if Trump succeeded it could trigger a crisis in American institutions.