WASHINGTON (AFP) - A second woman has made allegations of an affair with US President Donald Trump, describing complex legal and financial agreements in an alleged bid to cover it up.

Former Playboy model Karen McDougal claims that she and Trump had a sexual relationship in 2006, months after first lady Melania Trump gave birth to the President's youngest son.

The White House did not immediately reply to a request for comment, but in a statement to NBC a spokesman said the President had previously denied having a relationship with McDougal, calling the claims "fake news."

According to the New Yorker, the nine month relationship ended quietly, but years later - during the 2016 presidential campaign - McDougal sold her story.

The New Yorker reported that on Aug 5, 2016, McDougall agreed to give the company which owns the National Inquirer tabloid exclusive rights over "any romantic, personal, or physical relationship she has ever had with any 'then-married man'."

The deal is alleged to have been worth US$150,000 (S$200,000), but the story never ran.

The National Enquirer is owned by David Pecker, who has claimed to be a friend of Trump's. The tabloid endorsed Trump's bid for the presidency.

The company did not reply to a request for comment.

"I'm the one who took it, so it's my fault, too. But I didn't understand the full parameters of it," McDougal told the New Yorker of the alleged payment.

The model's story strongly echoes allegations of an affair between Trump and the porn star Stephanie Clifford - known as Stormy Daniels - during the same period.

In that case, the president's personal lawyer admitted to paying Daniels US$130,000 but refused to say why.

Good governance groups believe that could constitute a campaign donation and could breach election financial rules.