In the tape obtained by the channel network on Tuesday both Trump and Cohen discuss a transfer of money to a company for "info regarding our friend David" -- an apparent reference to David Pecker, the CEO of American Media Inc. which owns the National Enquirer.

The audio, made in September of 2016, is the first evidence that Trump knew about the payment.

"I need to open up a company for the transfer of all of that info regarding our friend David," Cohen said in the recording. Trump interrupts Cohen asking: "What financing?"

Cohen then tells Trump, "We'll have to pay" and Trump is heard saying "pay with cash". Cohen is heard saying "no no no".

American Media, Inc. allegedly spent $150,000 in August of 2016 for a story from Karen McDougal, the playmate who claimed she had a 10-month affair with Trump.

But the expose never ran.

McDougal's sued the company earlier in 2018 for the rights to tell her story.

Her lawyers claimed that the purchase was part of a "catch-and-kill" strategy to bury her tale and protect then-candidate Trump from negative press.

The lawsuit was eventually settled and freed McDougal from the contract which she claimed she was "misled into signing".

Trump's lawyer Rudy Giuliani, however, has refuted all payment claims, the New York Post reported.

Cohen's lawyer Lanny Davis, who provided the audio tapes to the network, said it showed his client knows the truth about Trump.

"This is about honesty versus false disparagement of Michael Cohen," Davis told CNN.

"Why is Giuliani out falsely disparaging Michael Cohen -- because they fear him… They fear that he has the truth about Donald Trump.

"The truth is that when Donald Trump said ‘cash' which Rudy Giuliani knows that only drug dealers and mobsters talk about cash, it was, you heard Michael Cohen… say what? ‘No, no, no, no'."

The tapes were among others seized by federal authorities in a raid of Cohen's home and office.

CNN presenter Chris Cuomo tweeted on Tuesday: "Full audio: Presidential candidate Trump is heard on tape discussing with his attorney Michael Cohen how they would buy the rights to a Playboy model's story about an alleged affair Trump had with her years earlier, according to the audio recording.