US President Donald Trump is being investigated by the Federal Bureau of Investigation for a potential obstruction of justice related to the ongoing inquiry into Russian meddling in last year's election, according to media reports in the country.

And on Monday, a close friend of Trump's said the president is considering firing Mueller, a move that echoes Richard Nixon ordering the termination of the special prosecutor during the Watergate scandal. The comments follow Trump's statement on Friday that "I'll tell you about that maybe sometime in the near future", "If there are [tapes]", Mudd continued, "what about all the times he may have taped [Attorney General]?"

Mueller was appointed by Deputy Attorney General Rod Rosenstein.

The White House did not immediately respond to questions about Ruddy's claims. Though Ruddy was at the White House earlier in the day, those aides said he did not meet with Trump, but White House Chief Strategist Steve Bannon, a former conservative media leader himself.

Donald Trump fired FBI Director James Comey, and now may fire special counsel Robert Mueller who is also conducting an investigation into Trump's Russian Federation connections.

"Republicans are delusional if they think the special counsel is going to be fair", Gingrich tweeted.

"The attorney general is the one who has to fire him", said CNN's senior legal analyst Jeffrey Toobin on "Anderson Cooper 360".

After Comey's testimony, Trump said he had been vindicated because his former FBI director confirmed telling Trump on three occasions that he was not under investigation. Ruddy said he thought firing Mueller would be a "significant mistake".

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Ruddy said in an interview Monday with Judy Woodruff of PBS, "I think he's weighing that option".

Mr Rosenstein has also acknowledged that "theoretically" Mr Mueller could be removed from the position as special counsel, potentially undermining his investigation.

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

The Post report cited anonymous sources who were briefed on requests made by investigators.

"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.

They say Mr Trump did not collude with Russian Federation and see the investigation as a politically-motivated sham that handicaps his ability to execute his agenda, according to one person who advises the White House on how to handle the probe.

Rep. Adam Schiff, of California, the top Democrat on the Intelligence Committee, warned Trump that dismissing Mueller would ultimately be futile, saying "Don't waste your time".