The conversation took place at the Conservative Political Action Conference (Cpac) in the US capital, the former Ukip leader claimed.
The pair were pictured at the meeting, smiling with their thumbs raised.
"I was talking to him about Vietnam, where he had said that a bad deal was on the table so sometimes you have to walk. That was the exact quote from Trump." Mr Farage told The Daily Telegraph.
He likened the Brexit negotiations to the US leader's recent denuclearisation summit with North Korea in Vietnam.
"I said in the case of Vietnam that no deal was better than a bad deal and I gave my opinion that the same principle applied to Brexit," he said. "I think if you read the comments from his ambassador in London, I don't think it takes much reading between the lines. This American administration firmly believes in the nation state, not supranational structures and this administration are hugely keen on the defence, security and indeed business relationships that exist between our two countries.
"And I think it's fair to say they see Brexit as a great opportunity."
Mr Trump became friends during his campaign when the former Ukip leader, dubbed "Mr Brexit", was greeted at a rally in Mississippi before the 2016 election.
The two were also pictured just after the election, at Trump tower in New York, where Mr Farage appeared to be spearheading a new relationship between the UK and US.
Mr Trump has spoken highly of Mr Farage in the past, stating that he would do "a great job" as British ambassador to the United States.
The president had urged Theresa May not to walk away from a deal with the European Union outside Chequers in July 2018 - though he has been critical of the Brexit deal, warning it will limit a US-UK free trade deal.
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