(CNN) Can President Donald Trump dismiss special counsel Robert Mueller, who is appointed to lead the FBI investigation into Russia's potential ties to the 2016 election?

Ruddy, who had been at the White House Monday, told PBS' Judy Woodruff that "I think he's considering perhaps terminating the special counsel."

"I think he's weighing that option," he said referring to Trump.

Chris Ruddy to @JudyWoodruff : President Trump is considering firing special counsel Robert Mueller, who he considered for another position. pic.twitter.com/X4IIHlh8at

A source close to the President told CNN's Jim Acosta that Trump is being counseled to steer clear of such a dramatic move like firing the special counsel.

"He is being advised by many people not to do it," the source said.

Who can fire Mueller?

Technically, it's up to the attorney general to decide what to do with the special counsel.

"The attorney general is the one who has to fire him," said CNN's senior legal analyst Jeffrey Toobin on "Anderson Cooper 360." "(Attorney General) Jeff Sessions is recused here, so it would be up to (Deputy Attorney General) Rod Rosenstein, who was the person who just appointed Bob Mueller a couple of weeks ago."

Sessions previously recused himself from any involvement in the Russia investigation due to his role as a prominent campaign adviser and surrogate.

So that would leave such a decision to Rosenstein, who just appointed Mueller on May 17 to oversee the federal investigation into Russian interference in the 2016 election.

Why would Trump consider firing Mueller?

Mueller has been widely respected by many in Washington from both sides of the aisle, but not everyone is a fan.

Since being appointed special counsel in May, Mueller has built a team of formidable legal minds who've worked on everything from Watergate to Enron.

He brought on three partners from his former law firm, WilmerHale, with significant litigating experience in high-stakes cases.

JUST WATCHED Special counsel members donated to Dems Replay More Videos ... MUST WATCH Special counsel members donated to Dems 02:26

But three of the five lawyers brought by Mueller have donated overwhelmingly to Democrats, according to a CNN analysis of Federal Election Commission records.

-- James Quarles contributed $32,800 to Democrats and $2,700 to Republicans from 1988 to 2016.

-- Jeannie Rhee contributed $16,450 to Democrats from 2008 to 2016.

-- Andrew Weissmann previously gave $2,300 to Barack Obama's first presidential campaign in 2008 and $2,000 to the Democratic National Committee in 2006.

Former House Speaker Newt Gingrich, an informal adviser to the President, questioned whether the special counsel investigation would be impartial. "Republicans are delusional if they think the special counsel is going to be fair. Look who he is hiring.check fec reports. Time to rethink," he tweeted.

Republicans are delusional if they think the special counsel is going to be fair. Look who he is hiring.check fec reports. Time to rethink. — Newt Gingrich (@newtgingrich) June 12, 2017

Last month, Gingrich had tweeted: "Robert Mueller is superb choice to be special counsel. His reputation is impeccable for honesty and integrity."

Robert Mueller is superb choice to be special counsel. His reputation is impeccable for honesty and integrity. Media should now calm down — Newt Gingrich (@newtgingrich) May 18, 2017

Why would Trump's friend discuss this publicly?

This is unclear.

"Mr. Ruddy never spoke to the President regarding this issue," White House press secretary Sean Spicer said. "With respect to this subject, only the President or his attorneys are authorized to comment."

Deputy White House press secretary Sarah Huckabee Sanders said simply: "Chris speaks for himself."

Ruddy told PBS he thinks firing Mueller "would be a very significant mistake, even though I don't think there's a justification ... for a special counsel."

Several theories abound so far.

Matt Lewis, a CNN political commentator, said Trump has a pattern of surprise moves, such as the firing of former FBI Director James Comey.

"In this case, we have what could serve as a trial balloon," he said on "Anderson Cooper 360," suggesting that it might be a way to test public reaction.

Would there be a Russian investigation if Mueller is fired?

JUST WATCHED Schiff: Echoes of Watergate getting louder Replay More Videos ... MUST WATCH Schiff: Echoes of Watergate getting louder 03:01

After news of Ruddy's interview surfaced, Rep. Adam Schiff, the top Democrat on the House intelligence committee, tweeted: "If President fired Bob Mueller, Congress would immediately re-establish independent counsel and appoint Bob Mueller. Don't waste our time."

If President fired Bob Mueller, Congress would immediately re-establish independent counsel and appoint Bob Mueller. Don't waste our time. — Adam Schiff (@RepAdamSchiff) June 12, 2017

Schiff told CNN's Anderson Cooper if Mueller was ousted, Congress would have to re-establish the Independent Counsel Act that expired following the impeachment of President Bill Clinton.

"We're not going to let the President choose who conducts this investigation," he said.

The act was widely criticized after Kenneth Starr's lengthy investigation into Clinton, and in 1999, Congress allowed the independent counsel provisions of the law to lapse.

While in theory it is possible that Congress could reauthorize the independent counsel law, it would not necessarily be smooth sailing given that Republicans control Congress.

CORRECTION: This story has been updated to accurately reflect the period during which Quarles made his donations.