Britain's intelligence agency, GCHQ, learned of the potential ties as early as the end of 2015, according to an April 13 report from The Guardian. The source added, "This is between people in the Trump campaign and agents of [Russian] influence relating to the use of hacked material".
The agencies tell CNN they were not targeting the president.
"If foreign intelligence agencies share information with USA intelligence, and it's relevant to the investigation, then of course the intelligence committee will look at it", a source close to the Senate investigation told CNN.
But according to the report, the multiple probes into the matter got off to a slow start.
The information gathered by GCHQ - described by one source as the "principal whistleblower" - was said to have been picked up as part of the routine surveillance of Russian intelligence assets. He also weighed in on the president's claim that Barack Obama ordered British intelligence agency GCHQ to illegally wiretap Trump Tower during the campaign.
"The message was: 'Watch out. There's something not right here'".
According to one source, Robert Hannigan, who at the time was director of GCHQ, "passed material in summer 2016 to the Central Intelligence Agency chief, John Brennan".
A number of inquiries are now under way in Washington into Trump campaign officials and Moscow, including an FBI-led counter-espionage investigation and inquiries by both the House and Senate intelligence committees.
Over the next six months, until summer 2016, a number of western agencies shared further information on contacts between Trump's inner circle and Russians, sources said.
This is roughly around the same time that the Federal Bureau of Investigation obtained an order from the Foreign Intelligence Surveillance Act (FISA) court to surveil Trump adviser Carter Page, which the Washington Post broke news of on Wednesday.
Britain's Government Communications Headquarters became aware of suspicious "interactions" between associates of Donald Trump and suspected or known Russian operatives in late 2015, The Guardian reported on Thursday.