He served the bureau for 12 years during the administration of President George W. Bush and President Barack Obama.
A report in The New York Times said the president had indeed weighed the possibility, was dissuaded by staff, and has since landed on the idea of simply pressuring Mueller by letting him know he could be fired.
A presidential spokesperson responded with a qualified endorsement Tuesday: "While the president has the right to [fire Robert Mueller], he has no intention to do so", Sarah Huckabee Sanders said in response to a reporter's question.
Mr Trump does not have the authority to dismiss Mr Mueller, and he would have to ask Mr Rosenstein, who appointed the special counsel, to do so.
Ruddy appeared on PBS Monday night to reveal that President Donald Trump may be looking to fire Mueller, who is conducting the investigation into the president's campaign ties to Russian Federation. Jeanne Shaheen, a New Hampshire Democrat, whether he has seen good cause to fire Mueller. He later noted that it was up to Mueller to determine whether the issue might be part of his investigation, adding he thought Mueller "ought to review that".
The firing would have to be carried out by Rod Rosenstein, deputy attorney general, though regulations could be "set aside", the AP reported.
"I think it would be odd [Mueller] would have a confidential conversation and then, a few days later, become the prosecutor of the person he may be investigating", Ruddy said. They will also ask about his decision to recuse from an investigation into possible ties between Moscow and associates of President Donald Trump.
Newsmax Media CEO Christopher Ruddy stood by his claims after the White House downplayed his comments and suggested he did not know what he was talking about.
For many, the prospect of Mueller's firing immediately brought to mind the 1973 dismissal of special prosecutor Archibald Cox during the Watergate scandal.
Trump confirms he's under investigation, fires angry tweets
The Twitter attacks came as Vice President Mike Pence hired a personal lawyer to represent him in the intensifying investigation. Rosenstein, who would be responsible for actually dismissing Mueller, told US lawmakers he would fire him only with good cause.
Nathan Beaulieu traded to Sabres
He also opened the regular season on Montreal's top pairing with Shea Weber , but was quickly moved in favour of Alexi Emelin. Beaulieu makes sense for the Sabres, though, as he's a smart two-way player who can work on the man advantage.