The former Democratic president made the claim under oath last week in a videotaped deposition to the House of Representatives Oversight Committee, released on Monday.
Clinton said Trump brought up Epstein at a golf tournament in 2002 or 2003, after Clinton had left office and more than a decade before Trump was elected president.
"Somehow he knew I had flown in Jeffrey Epstein's aircraft," Clinton told the committee.
"He said, 'You know, we had some great times together over the years, but we fell out all because of a real estate deal'.'"
Trump has said the relationship soured after Epstein hired young women who worked at Trump's Mar-a-Lago club.
Clinton said the exchange didn't lead him to believe Trump was involved with anything improper involving Epstein.
The White House did not immediately respond to a request for comment.
Both Clinton and Trump associated with Epstein before the well-connected financier pleaded guilty in 2008 to soliciting prostitution from a minor.
Both have repeatedly said they did not see any evidence of sex trafficking, and neither has been accused by authorities of criminal activity related to Epstein, who entertained a long list of business and financial leaders at his lavish residences in New York, Florida and the Caribbean.
Epstein was arrested again in 2019 and died in prison while facing federal sex-trafficking charges. His death was ruled a suicide.
Under Trump, the Justice Department has released millions of records from its investigations into Epstein, including photos of Clinton with women whose faces have been redacted.
Clinton has repeatedly denied wrongdoing and has said he regrets his association with Epstein.
In last week's testimony, Clinton said he was introduced to Epstein by his former Treasury Secretary Larry Summers, who described Epstein as a donor who was willing to fly Clinton and his staff around the globe as he set up a charitable AIDS foundation.
Clinton said he flew on Epstein's jet on trips to Asia, Africa and Europe, and once from Florida to New York, but moved on to other donors after 2003.
"I thought Mr Epstein was an interesting man, but I didn't think he was really interested in what I was doing," Clinton said.
Clinton said he never had sexual contact with anyone introduced by the late financier or his associate Ghislaine Maxwell, but did receive a neck massage from a flight attendant later identified as an Epstein abuse survivor.
Clinton said he did not know that Epstein had abused girls whom he had recruited as masseuses.
"I didn't think it was anything unusual. I can't tell you how many airplanes I've been on where rich people asked me to go and they had someone offering massage," he said.
"All these boats that you go on and all that, they all do that. And usually I don't do that," he said.
Clinton said he never visited Epstein's Caribbean island and did not know that Epstein had visited the White House 17 times during his 1993-2001 presidency.
The Republican-led panel also subpoenaed former Secretary of State Hillary Clinton, who testified last week that she did not recall ever meeting Epstein.
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