The company has approached Ms McDougal about extending her contract barring her from talking about Mr Trump in recent months as the behind-the-scenes negotiations to keep porn star Stormy Daniels' allegation of a Trump affair have been made public, the magazine reported.
The National Enquirer published harshly critical articles on Hillary Clinton during the presidential campaign, but AMI denies paying anyone to protect Trump from damaging stories. The reporting echoed a Wall Street Journal story from November, mere days before the election, which said AMI paid her for the story of the affair but didn't publish it.
Reporters travelling with Mr. Trump were prevented from seeing the First Lady arrive on the plane, but she did exit the plane at West Palm Beach with him. The National Inquirer is owned by David Pecker who is claimed to be a friend of Trump.
The White House is denying a new report that President Trump had an extramarital affair before he launched his political career.
In McDougal's account of her affair with Trump, the model said that she ended it in part after she started feeling guilty about it and after Trump made an offensive comment about her mother's age as well as a vulgar remark about the anatomy of black men. Daniels has allegedly been paid off to stay mum about her "affair' with Trump sending a new catch phrase from tabloid journalism swirling into the mainstream news circuit - "catch and kill". She alleges Trump tried to avoid creating a record that might expose their relationship by having her pay for her own flights and then reimbursing her. She said she would see Trump every time he was in Los Angeles.
"McDougal joined Trump at the American Century Celebrity Golf Championship, at the Edgewood Resort, on Lake Tahoe" in July 2006, according to the New Yorker story.
A month back when, Stormy Daniels, adult film star disclosed that she received a payment of $130,000 (£95,000) from Trump's personal lawyer to prevent publicly discussing the alleged sexual encounter. The magazine said the description of the affair comes from an eight-page, handwritten chronicle that McDougal had written and shared with a friend. Detailing the alleged affair, which reportedly took place less than two years after Donald and Melania trump married, when their son Barron was just an infant.
Orange County restaurateur Summer Zervos, a former contestant on "The Apprentice", has accused Trump of trying to force himself on her in 2006.
In one instance, when McDougal toured Trump Tower, she recalled a moment when Trump pointed out Melania's separate bedroom. "I looked at him (and felt sad) and said, "No thanks - I'm not 'that girl.' I slept w/you because I like you - NOT for money" - He told me, 'you are special'".
"I know it's a different circumstance, but I just think I feel braver", she added, and doesn't recommend other women sign agreements limiting their freedom of speech.