The Oscar-winning actress, 57, said in an interview on Swedish television that the president asked her out in 1998.
"I wish I had [accepted]," the "Beauty and the Beast" star joked with the hosts. "Think of the stories!"
"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 then replied, "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.'"
She never did.
Trump went on to marry his third wife, Melania. Meanwhile, Thompson married her "Sense and Sensibility" co-star Greg Wise, with whom she has a daughter and a son.