According to the document, which McDougal confirmed she wrote, the former Playmate met the NY billionaire in 2006 when he was at the Playboy Mansion in Los Angeles filming an episode of "The Apprentice".
Journalist Ronan Farrow obtained an eight-page, handwritten note from Ms McDougal's friend detailing their relationship.
Farrow wrote: "As McDougal was getting dressed to leave, Trump did something that surprised her".
Trump was at the Playboy Mansion in Los Angeles that June filming an episode of The Apprentice.
According to the New Yorker, McDougal had claimed that the businessman was so taken with her that one Playboy exec had told her: "I think you could be his next wife".
She said he always ordered the same meal - steak and mashed potato - and never drank, describing him as "charming" and "polite". It also contracted her to write a fitness column.
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.
Trump denied the New Yorker report, as the White House has done with news about Daniels, despite the fact that Trump lawyer Michael Cohen confirmed that he paid her $130,000 out of his own pocket.More news: Prince Harry and Meghan Markle delight fans in Scotland
Jerry George, a former senior editor for American Media, told The New Yorker that Pecker routinely buys and kills stories, and also protects Trump, who he considers a friend. "No paper trails for him", she wrote, according to Farrow. The real estate mogul hit on her and asked for her phone number, before they met up for dinner and sex at the Beverly Hills hotel.
This is the second time this week the first lady has seemingly removed herself from the public sphere when conversation has turned to discussion of Trump's alleged affairs.
McDougal ended the affair in April 2007, after nine months.
The National Enquirer's publishing company paid McDougal $150,000 for her story about having an affair with Trump (left) while he was married to his wife Melania (right) - but never ran it, sources told the Wall Street Journal.
Maggie Haberman, the White House correspondent for the New York Times, pointed out an interesting shift in the language used by the White House in their denials of both stories. Those promises she said, were not fulfilled, and she now regrets signing the deal.
Farrow, the New Yorker reporter, first broke the stories about sexual abuse claims against Weinstein.
"This is a favorite tactic of the C.E.O. and chairman of A.M.I., David Pecker, who describes the President as 'a personal friend, '" Farrow wrote.
McDougal, a Republican, said she didn't realize the scope of the gag agreement she originally signed.