Federal investigators have seized audio tapes in which US President Donald Trump and his lawyer Michael Cohen discuss making payments to a Playboy model with whom Mr Trump allegedly had an extramarital affair.

The tapes, recorded by Mr Cohen two months before the US election in November 2016, were revealed by The New York Times on Saturday morning (AEST).

Mr Trump’s attorney, former New York mayor Rudy Giuliani, confirmed the existence of the tapes but said no payment was ever made.

FBI agents seized the recordings during an April raid of Mr Cohen’s office as part of a Justice Department investigation into whether Mr Trump’s longtime lawyer paid women to prevent damaging stories about the presidential candidate being published before the election – an act Mr Trump’s foes have argued could be prosecuted as a breach of campaign finance laws.

According to The New York Times report, Mr Trump and Mr Cohen were recorded discussing a payment to former model Karen McDougal, who claims she had a year-long affair with Mr Trump in 2006 after his wife Melania gave birth to their son Barron.

Karen McDougal says she was paid hush money to stay silent about an extended affair with Donald Trump.

Ms McDougal was paid $US150,000 ($202,000) for her story by American Media Inc (AMI), the parent company of The National Enquirer, a pro-Trump supermarket tabloid, in August 2016.

The report was never published in a practice called “catch and kill” which prevents stories from becoming public.

Mr Giuliani maintained the President had done nothing wrong and said Mr Trump had no prior knowledge of the magazine payment.

“Nothing in that conversation suggests that he had any knowledge of it in advance,” Mr Giuliani said.

He confirmed the President and his lawyer discussed paying Ms McDougal to buy her story to ensure the alleged affair was never revealed, but the payment wasn’t made.

According to The Washington Post, Mr Trump discussed purchasing the rights to Ms McDougal’s story from AMI and urged Mr Cohen to make sure he properly documented the agreement.

Mr Trump’s lawyer confirmed the existence of the tapes recorded by Mr Cohen. Photo: Getty

The revelation comes as Mr Cohen looks increasingly likely to cooperate with investigators.

Once considered Mr Trump’s longtime confidant who promised he would remain loyal to the president, the relationship has soured in the wake of the April raids.

In an interview with ABC News last month, Mr Cohen said his family, not Mr Trump, had his first loyalty.

“My wife, my daughter and my son have my first loyalty and always will,” he said. “I put family and country first.”

Ms McDougal is the second woman to have reportedly been paid hush money after coming forward with accusations of sexual encounters with Mr Trump, the first being adult actress Stormy Daniels.

The investigation into Mr Cohen began with Special Counsel Robert Mueller’s investigation into the Trump campaign’s ties to Russia.

Mr Mueller referred Mr Cohen’s case to federal prosecutors in New York when it became more about the lawyer’s personal dealings, including payments to women reportedly involved with Mr Trump.

Ebony Bowden contributed reporting from New York City.