Presidential candidate Donald Trump is heard on tape discussing with his lawyer 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 of the conversation aired exclusively on CNN's Cuomo Prime Time.

The recording offers the public a glimpse at the confidential discussions between Mr Trump and Cohen, and it confirms the man who now occupies the Oval Office had contemporaneous knowledge of a proposal to buy the rights to the story of Karen McDougal, a woman who has alleged she had an extramarital affair with Mr Trump about a decade ago.

Mr Cohen told Mr Trump about his plans to set up a company and finance the purchase of the rights from American Media, which publishes the National Enquirer .

US President Donald Trump has been recorded discussing paying for a Playboy models's story. Picture: AAP (AAP)

"I need to open up a company for the transfer of all of that info regarding our friend David," Cohen said in the recording, likely a reference to American Media head David Pecker.

Mr Trump interrupts Cohen asking, "What financing?" according to the recording. When Mr Cohen tells Mr Trump, "We'll have to pay" Mr Trump is heard saying "pay with cash". But the audio is muddled and it's unclear whether he suggests paying with cash or not paying. Mr Cohen says, "no, no" but it is not clear what is said next.

No payment was ever made from Mr Trump, Rudy Giuliani, the President's attorney, has said. Mr Giuliani has previously acknowledged that the recorded discussion related to the buying the story rights.

The recording, which was provided to CNN by Mr Cohen's lawyer Lanny Davis, was made in September 2016.

Karen McDougal claims she had an affair with Mr Trump a decade ago. (CNN)

"What is this about? This is about honesty versus false disparagement of Michael Cohen. Why is Giuliani out falsely disparaging Michael Cohen - because they fear him," Davis said on Cuomo Prime Time .

"What do they fear, Chris? Why am I representing him? They fear that he has the truth about Donald Trump. He will someday speak 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.'"

Mr Davis later added: "Ladies and gentlemen, if you voted for Donald Trump, listen to the tape and ask yourself: Is Donald Trump lying when he said he didn't use the word 'cash' and accuses Michael Cohen of using the word 'cash'? Cohen has been disparaged. Cohen has been insulted and called all sorts of things by people around Donald Trump."

Alan Futerfas, a lawyer for Trump Organization, refuted that Mr Trump was offering a cash payment.

"Whoever is telling Davis that cash in that conversation refers to green currency is lying to him," Futerfas told CNN. "There's no transaction done in green currency. It doesn't happen. The whole deal never happened. If it was going to happen, it would be a payment to a large company that would obviously be accompanied by an agreement of sale. Those documents would be prepared by lawyers on both sides."

Secret recordings have been released between Mr Trump and his personal lawyer Michael Cohen. (AAP) (AAP)

Cash, in the conversation, was in reference to how a deal would be financed, Futerfas added.

"The word cash came up in the context of the distinction between financing, which is referenced, and no financing, which means a full payment, a total one-time payment. That's the context in which the word cash is used," he said. "Anyone who knows anything about the company or how the President does business knows there is no green cash. Everything is documented. Every penny is documented."

Court filings said federal prosecutors have obtained 12 audio recordings from the FBI raids on Mr Cohen earlier this year . CNN previously reported that Mr Trump's lawyers waived attorney-client privilege on the President's behalf regarding the recording involving him personally.

The audio of Mr Trump was obtained exclusively by CNN. (AAP)

The discussion relates to whether Mr Trump should buy the rights of the story from American Media, which paid McDougal $150,000 in August 2016 for her story about an alleged 10 month affair with Trump. The story was never published by AMI.

In addition to discussing the McDougal payment, Mr Trump and Mr Cohen are overheard running through a list of potential legal issues, including contesting a New York Times request to unseal divorce records from Trump's first wife Ivana as well as more mundane matters such as polling numbers and Trump surrogate Pastor Mark Burns.