The 57-year-old Oscar-winning actress, said in an interview on Swedish television that the president asked her our in 1998.
"I wish I had [accepted]," the Beauty and the Beast star joked with the hosts. "Think of the stories!"
According to the actor, the invitation came when she was filming the 1998 film Primary Colors in Los Angeles. Ironically, the film was loosely based on Bill Clinton's 1992 presidential campaign, and the Love Actually star was playing a character modeled on Hillary Clinton.
Trump was single, having announced his separation from second wife Marla Maples in May 1997 and Thompson had just received her divorce decree from her ex-husband Kenneth Branagh.
"The phone rings in my trailer, which it’s never done before," Thompson recalled.
"I lift up the phone. 'Hi, it’s Donald Trump here.' I said, 'Really? Well, can I help you?’" she continued.
"He said, 'Yeah, I wonder if I could offer you some accommodation in one of my Trump Towers. They’re really comfortable.' And I said, 'Why are you offering me somewhere to stay, in my trailer?'" Thompson said.
According to Thompson, Trump said, "I think we would get on very well, maybe we could have dinner sometime."
Thompson said she was shocked.
"I didn’t know what to do with myself," she said. "I was on my own and I just said, ‘OK, well, um, I’ll get back to you.'"
However, she never did.