FBI agents were so concerned about Donald Trump's behaviour that they investigated whether the US president was working on behalf of the Kremlin, a report in the New York Times has said, citing former law enforcement officials.

The probe followed Trump's decision to fire FBI chief James Comey, but reportedly came amid a backdrop of suspicions dating back to his successful 2016 campaign for the presidency.

Comey, who was sacked in May 2017, had opened an FBI investigation into whether Russia meddled in the 2016 election and whether the Kremlin officials colluded with the members of Trump's team.

After his dismissal, Trump faced accusations of obstruction of justice, which loudened after he fired FBI deputy director Andrew McCabe the following year.

McCabe said he believed Comey was fired because he refused to give in to Trump's requests to kill the probe.

Comey has since condemned Trump as 'morally unfit' to hold the office of president, and said there was "certainly some evidence of obstruction of justice".

Friday's New York Time's report said the intelligence officials had to consider whether the president's actions had constituted a "threat to national security".

The report says no evidence has publicly emerged that Trump was in contact with or took direction from Russian officials, and FBI officials refused to comment on the alleged investigation.

Trump on Saturday slammed the NYT piece on Twitter, writing that an investigation was opened "for no reason and with no proof".

"Wow, just learned in the Failing New York Times that the corrupt former leaders of the FBI, almost all fired or forced to leave the agency for some very bad reasons, opened up an investigation on me, for no reason & with no proof, after I fired Lyin’ James Comey, a total sleaze!" Trump wrote.

Wow, just learned in the Failing New York Times that the corrupt former leaders of the FBI, almost all fired or forced to leave the agency for some very bad reasons, opened up an investigation on me, for no reason & with no proof, after I fired Lyin’ James Comey, a total sleaze! — Donald J. Trump (@realDonaldTrump) January 12, 2019

Bruce Fein, former US associate deputy attorney general and a constitutional lawyer, told Al Jazeera that Trump could expect subpoenas regarding this investigation as early as next week.

"Even though this wasn't a crime necessarily, it certainly bares on the fitness of the president for office which means impeachment covers actions that are short of criminal activity," Fein said.

"I can guarantee you that the house government affairs and oversight committee will probably issue subpoenas on Monday to get to the bottom of this - why did the FBI think that the evidence was credible enough to suggest that Mr. Trump was actually spying on the country on behalf of Russia?"

Mueller probe

The investigation into alleged Russian meddling was taken over by special counsel Robert Mueller, himself a former director of the FBI, after Comey's firing.

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His investigation has resulted in criminal prosecutions and indictments of several former Trump aides, including his ex-campaign chair Paul Manafort, ex-NSA Michael Flynn and former lawyer Michael Cohen, among others.

Trump has dismissed the probe as a "witch-hunt" and many critics fear that he is paving the way to fire Mueller.

The US president has not yet addressed Friday's New York Times report yet but his lawyer, former New York City Mayor, Rudolph Guiliani, said that the fact no findings had been published "means they found nothing".