The Times says it is unclear whether Mr Mueller is still pursuing the counterintelligence angle.
Mr Trump's lawyer, Rudy Giuliani, told the Times that he had no knowledge of the inquiry.
And Trump's former presidential campaign chair, Paul Manafort, has been convicted in one case brought by Mueller and pleaded guilty in another, over financial crimes related to his work in Ukraine before the 2016 campaign, and for witness tampering.
Driver crashed while participating in 'Bird Box Challenge'
A 12-year-old U.S. girl gave herself burns to about 50 per cent of her body last year. That's when she veered into oncoming traffic and collided with another vehicle.
Comey spoke after a spurt of anti-FBI tweets from the president in December alleged that the investigative body abused its powers in probing his former personal lawyer Michael Cohen and his former national security adviser Michael Flynn. NBC News reported that Deputy Attorney General Rod Rosenstein plans to step down after Mueller completes the investigation and expects that he will be able to leave by March.
"Not only would it be an issue of obstructing an investigation, but the obstruction itself would hurt our ability to figure out what the Russians had done, and that is what would be the threat to national security", Baker said in his testimony, portions of which were read to The New York Times.
The grand jury empaneled by the special counsel has been extended for another six months, however, signaling that the probe may continue beyond the winter.
Also fueling the FBI's concerns was Christopher Steele's "dirty dossier" of unsubstantiated allegations, which had been funded by Democrats but at that point was justifying probes across the Justice Department.
"What we're reporting tonight is the investigation initially ... was much bigger than that was looking that question of Trump's ties to Russian Federation", the reporter added.
"I think we have wasted enough time on this witch hunt and the answer is probably, we're finished", President Trump said, though he added "I can change my mind".
"Unlike President Obama, who let Russian Federation and other foreign adversaries push America around, President Trump has actually been tough on Russian Federation", she said.