But that would be a huge mistake, Republican lawmakers said Monday.

“It would be a disaster,” said Sen. Lindsey Graham (R-S.C.) “There’s no reason to fire Mueller. What’s he done to be fired?”

Mueller’s investigation is widely considered the most threatening to Trump’s presidency. It encompasses questions about whether Trump associates colluded with Russians to influence the 2016 election — and, more recently, whether Trump himself may have obstructed the FBI’s inquiry when he abruptly fired former FBI director James Comey. It is also a probe that is largely out of Trump’s control.

The White House late Monday said in a statement that Ruddy “never spoke to the President regarding this issue. With respect to this subject, only the President or his attorneys are authorized to comment.”

On Capitol Hill, Mueller’s appointment seemed to calm nerves after the firing of Comey. A former FBI director who served for 12 years under Presidents George W. Bush and Barack Obama, Mueller won bipartisan praise last month, when he was appointed by Deputy Attorney General Rod Rosenstein to oversee the Russia probe.

Sen. Susan Collins (R-Maine) said the notion firing Mueller, would “certainly be an extraordinarily unwise move.”

Collins and other Republicans said they had no indication Trump was considering firing Mueller. But lawmakers were taken by surprise last month when Trump fired Comey, who was then overseeing the Russia investigation. Comey himself poured fuel on the investigation last week when he testified that Trump repeatedly questioned him about the Russia probe — and asked him to end a related investigation into former national security adviser Michael Flynn — before firing him on May 9.

Comey also testified last week that shortly after Trump fired him, he steered the contents of several private memos to the press in order to prompt the creation of the special counsel probe. Comey has a long-term friendship with Mueller, who has begun filling out his prosecutorial team with experienced hands.

Those facts have alarmed some allies of the president on the hill.

“Bob Mueller’s obviously intent on hiring people who are antagonistic toward this administration,” said Rep. Trent Franks (R-Ariz.) “He’s one of Mr. Comey’s closest friends, and it looks like there’s a deliberate orchestration to damage or undermine the president regardless of the basic facts.”

So far, Franks appears to have a minority view among his colleagues. He said Mueller and Comey’s longstanding friendship “constitute an incontrovertible conflict of interest,” and he said it was time to end the “mindless charade.” But Franks stopped short of urging Trump to fire Mueller.

“I’m not sure I’ve developed an appropriate conviction on that yet,” he said.

Franks’ comments echoed similar criticisms lodged by Trump associates in recent days.

“Republicans are delusional if they think the special counsel is going to be fair,” former House Speaker Newt Gingrich said on Twitter on Monday. “Time to rethink.”

But overwhelmingly, GOP lawmakers heaped praise on Mueller and said they trusted him to lead a fair and thorough probe.

“I think there’s a lot of confidence in Mueller around here,” added Sen. Jeff Flake (R-Ariz.) “We’ve all dealt with him.”

And a number of GOP lawmakers, including Sen. John McCain, reiterated that they remain confident in him to lead an impartial investigation.

“He’s a very much trusted individual and had an outstanding record as head of the FBI,” McCain said.

Even some of Trump’s closest allies in Congress are warning against any rush to nix the Mueller probe.

“I think Bob Mueller’s as good as you’re going to find. I don’t see any reason to remove him now,” said Rep. Peter King (R-N.Y.), who has largely defended Trump throughout the investigation into potential Russia ties.

Asked whether Comey’s efforts to nudge DOJ to create a special counsel had tainted the probe, King said, “I think it would taint it more to remove him now.”

The warnings to Trump not to fire Mueller come as some of the president’s allies are working to drum up opposition to the special counsel.

Gingrich, who last month called Mueller a “superb choice” for special counsel, accused Mueller of hiring partisans” to run the investigation.

Several Trump allies blasted Mueller’s decision to hire investigators who have given campaign donations to Democrats, including Andrew Weissmann, who’s on detail from his post as head of the Justice Department’s criminal fraud division.

Attorney General Jeff “Sessions never should’ve recused himself,” conservative activist and Trump supporter Ann Coulter said on Twitter. “Now that we know TRUMP IS NOT UNDER INVESTIGATION, Sessions should take it back & fire Mueller.”