It is believed that the GCHQ never carried out a targeted operation against Trump or proactively sought information.
The alleged interactions were picked up as part of routine surveillance of Russian intelligence assets.
It is believed that the Dutch and France's spy agency also passed over information.
Britain's MI6 also played a role in intelligence sharing, a source said, but the spy agency declined to comment.
Trump and his Republican supporters want FBI and Congressional investigations to target claims that Obama spied on his successor, rather than Moscow's interference in the election.
Trump has repeatedly called the Russian interference story "fake news" while alleging, without offering evidence, that the previous administration of president Barack Obama spied on him and his campaign.
MI6's former chief Sir Richard Dearlove, described called Trump's wiretapping claims "simply deeply embarrassing for Trump and the administration".
'The only possible explanation is that Trump started tweeting without understanding how the NSA-GCHQ relationship actually works,' Dearlove told Prospect magazine.
His spokesman Sean Spicer complained Monday that US media was, in its focus on the Russia issue, pursuing the wrong story.
Spicer has also falsely claimed that the "British spying agency" GCHQ' has carried out surveillance of Trump during the campaign.
The allegations were called "utterly ridiculous" by a GCHQ spokesman, who said the claims "should be ignored".
The United States and UK have said that the GCHQ did play an early role in prompting the FBI's Trump-Russia investigation in late July 2016.
The agency was a "principal whistleblower", one insider told The Guardian.
It is believed that the FBI and CIA were slow to kickstart an investigation because US law prohibits them from surveilling private communications of American citizens without warrants.
"It looks like the [US] agencies were asleep," a source told The Guardian. "They [the European agencies] were saying: 'There are contacts going on between people close to Mr Trump and people we believe are Russian intelligence agents. You should be wary of this.'"
"The message was: 'Watch out. There's something not right here.'"
The White House on Wednesday tried to distance itself from a one-time campaign aide to Trump, Carter Page, after revelations that the FBI investigated him last year for ties to Russian intelligence.
The Washington Post reported that federal investigators obtained a rare warrant from the top-secret Foreign Intelligence Surveillance Court to monitor Page's communications - the first confirmation of government surveillance of Trump's team.
During the 2016 election campaign, then candidate Trump personally referred to Page as one of his foreign policy advisors.
It has now emerged that federal prosecutors and an intelligence court judge at least suspected the former Moscow-based banker was also working for, or with, the Russians.
The White House rushed to play down Page's ties to Trump and the campaign.
One current official told AFP that Page never met Trump, did not have a campaign pass and was only mentioned as an advisor because the billionaire candidate was under pressure to show he had a policy brain trust.
The official admitted that Page could have written policy memos for the campaign, but his name was only on a list of supposed advisors because of a recommendation from Sam Clovis, an Iowa conservative now working in Trump's Department of Agriculture.
Russia-US ties following Trump's election have been shattered by the congressional investigation into alleged ties between Trump's campaign associates and Russia.
The tense back-and-forth over last week's deadly chemical attack in Syria has added to the strain.
US Secretary of State Rex Tillerson warned Russian President Vladimir Putin in Moscow Wednesday that relations between Washington and Moscow, a key ally of the Damascus regime, were at a "low point".
Donald Trump took an optimistic tone toward US-Russia relations on Twitter Thursday - hours after saying they were at an "all time low".
