In a CNN interview, Ms McDougal said she would tell the first lady she was sorry for the alleged 10-month affair and she "wouldn't want it done to me".
She also revealed that she cried on the way home after Mr Trump offered her money during their first encounter.
The president and the White House have both denied the alleged affair.
"I'm sorry. I wouldn't want it done to me," she told CNN's Anderson Cooper on Thursday.
"When I look back, where I was back then, I know it's wrong," she said in an emotional plea. "I'm really sorry for that. I know it's a wrong thing to do."
Ms McDougal signed a deal worth $150,000 (£106,000) to tell her story exclusively to the tabloid newspaper, the National Enquirer, in 2016.
However, the article was never published and Ms McDougal insists she was tricked into silence about the relationship.
She is now suing the publication to end the deal.
Ms McDougal is one of three women who have launched law suits over affairs or sexual assault claims involving the president.
These are the other two:
The porn star: Stormy Daniels
Porn actress Stormy Daniels, whose real name is Stephanie Clifford, says she and Mr Trump had a sexual relationship lasting several months in 2006.
She says that she was paid $130,000 (around £92,000) by Mr Trump's lawyer to remain silent about the affair just before the 2016 election.
Ms Clifford has now filed a lawsuit which aims to scrap the agreement, which her lawyer says she was physically threatened into accepting.
Earlier this year, an interview she gave to InTouch magazine in 2011 about her alleged relationship with Mr Trump resurfaced.
A polygraph test from the interview obtained by CBS News concluded that she had been "truthful" in her account.
The president has denied any sexual relationship with the actress.
His lawyers are now suing Ms Daniels for $20m (£14m) for breaching the non-disclosure agreement.
An interview with Ms Daniels is due to air on CBS News on Sunday.
The Apprentice contestant: Summer Zervos
Summer Zervos, a former contestant on The Apprentice, was one of a number of women who made allegations of sexual misconduct against Donald Trump during the 2016 presidential race.
She accuses Mr Trump of sexually assaulting her at a Beverly Hills hotel in 2007.
Ms Zervos says that he groped her and "began thrusting his genitals" during a meeting to discuss employment opportunities.
While president-elect, Mr Trump dismissed the allegations against him and said that Ms Zervos and other accusers were "sick" and driven by fame, money or politics.
Ms Zervos filed a defamation law suit against Mr Trump in January 2017, but his lawyers argued that as the president he could not be sued.
A judge in New York has now overturned that decision, meaning that Ms Zervos's case against the president will continue.