The audio, which was secretly recorded in 2016, was provided to CNN by Lanny Davis, who represents Trump's former personal attorney Michael Cohen and was played on air Tuesday evening.
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The conversation between Trump and Cohen came weeks after the National Enquirer's parent company reached a $150,000 deal to pay former Playboy model Karen McDougal for her story of a 2006 affair, which it never published, a tabloid practice known as catch and kill. Trump denies the affair ever happened.
Cohen can be heard on the tape saying that he needed to start a company "for the transfer of all of that info regarding our friend David," a possible reference to David Pecker, Trump's friend and president of the National Enquirer's parent company, American Media Inc.
When Cohen begins to discuss financing, Trump interrupts him and asks, "What financing?"
"We'll have to pay," Cohen responded.
The audio is muffled, but can be heard saying to "pay with cash" and Cohen immediately says, "no, no." Trump can be heard after saying, "check."
Last week, Trump's attorney Rudy Giuliani said the recording would prove that "the president said it has to be done correctly and it has to be done by check."
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Giuliani provided a transcript to CNN that Trump told Cohen, "Don't pay with cash ... check."
"The transcript that we provided CNN accurately reflects the taped conversation," Giuliani told The Associated Press.
"Listen to the tape. Donald Trump is not shocked money is being paid about someone named Karen McDougal," Davis said during an interview with CNN. "
Davis said his client - who is under investigation by federal officials in New York - "has been disparaged and insulted and called all kinds of things."
"He's got truth on his side and he'll continue to tell the truth," Davis said.
American Media, Inc.'s payment effectively silenced McDougal through the election, though days beforehand news of the deal emerged in The Wall Street Journal. At the time, a Trump spokeswoman said his campaign had "no knowledge of any of this."