The 57-year-old British actress said on the Swedish show Skavlan that the 70-year-old businessman asked her to have dinner years before he married Melania Trump and became president.
"He asked me out once," Thompson shared.
"It's very funny. I was doing a film called 'Primary Colors' with John Travolta in Hollywood. I was in my trailer on the Universal lot, and I'd just been divorced. My decree nisi -- decree absolute -- had just come through the day before."
"The phone rings in my trailer, which it's never done before," she recalled.
"I lift up the phone -- 'Hi, it's Donald Trump here.' I said, 'Really? Can I help you?' He said, 'Yeah, I wondered if I could offer you some accommodation in one of my Trump [hotels]. They're really comfortable.'"
"I said, 'Why are you offering me somewhere to stay in my trailer?' [He said], 'Well, you know, I thought we would get on very well. Maybe we could have dinner sometime,'" she said. "I didn't know what to do with myself. I was on my own and I said, 'I'll get back to you.'"
Thompson, who split from ex-husband Kenneth Branagh in 1995, said she never took Trump up on his offer.
The actress married Greg Wise in 2003, while the now-president wed Melania Trump in 2005.
"You could be the first lady!" Skavlan host Fredrik Skavlan joked after Thompson's story.
Copyright 2017 United Press International, Inc. (UPI). Any reproduction, republication, redistribution and/or modification of any UPI content is expressly prohibited without UPI's prior written consent.