Former Playboy model Karen McDougal claims that she and Trump had a sexual relationship in 2006, which began 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 the New Yorker an unnamed a spokesperson said the president had 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.
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The deal is alleged to have been worth $150,000, but the story never ran.
"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 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 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 USD 130,000 but refused to say why.
Good governance groups believe that could constitute a campaign donation and could breach election financial rules.