The newspaper said Farage had not been accused of wrongdoing and was not a suspect or target of the US investigation. But it said he was "right in the middle" of the relationships being looked at.
The newspaper said the former leader of the UK Independence Party had "raised the interest" of FBI investigators due to his connections with Trump and Julian Assange's Wikileaks, which published leaked emails from the Democratic National Committee during the campaign.
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Farage said on Twitter it had taken him a long time to read the Guardian article because he was "laughing so much at this fake news".
"This hysterical attempt to associate me with the (Vladimir) Putin regime is a result of the liberal elite being unable to accept Brexit and Trump," he said.
"I consider it extremely doubtful that I could be a person of interest to the FBI as I have no connections to Russia."
Accusations that Russia interfered in the US 2016 presidential election have dogged Trump since he entered office and a former FBI chief, Robert Mueller, has been named as special counsel to investigate any collusion.
US intelligence agencies concluded that Russia used computer hacking, propaganda and misleading news reports designed to sway political opinion in an attempt to boost Trump's chances of winning the White House.
Trump has dismissed the notion that Russia played any role in his November election victory. Kremlin chief Vladimir Putin, a former KGB spy, has denied meddling in the US election.
CIA Director Mike Pompeo called Assange's Wikileaks a "hostile intelligence service" in April after it distributed material hacked from Democratic National Committee computers during the 2016 campaign.
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Pompeo said Russia's GRU military intelligence service had used Wikileaks to distribute the material and concluded that Russia stole the emails and took other actions to tilt the election in favor of Trump, a Republican, over Democratic candidate Hillary Clinton.
"One of the things the intelligence investigators have been looking at is points of contact and persons involved," the Guardian quoted one source as saying. "If you triangulate Russia, WikiLeaks, Assange and Trump associates the person who comes up with the most hits is Nigel Farage."
"He's right in the middle of these relationships. He turns up over and over again. There's a lot of attention being paid to him."
Farage, who campaigned for decades for Britain to leave the European Union, was a vocal backer of Trump, appearing on the campaign trail and meeting him in New York just days after the election victory.
Farage, who also attended Trump's inauguration in Washington, met Assange in March this year at the Ecuadorean embassy in London where the Wikileaks founder has been holed up for five years.
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