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"I know one, and it just didn't happen recently,"Cuban told CNN host Don Lemon. "I'd - my friend reminded and it was from 2000 and she - you know, I don't expect her to come forward. I wouldn't recommend she come forward."
The business mogul added that he also knows "somebody else" from two years ago "that won't come forward."
"So, you know, it's not anything that caught me by surprise," Cuban said. "I mean, that's what I can tell you. I can tell you - my friend that was dating this one woman, you know, just - you know, reminded me the story they told me right after it happened and put it all down in detail. And, obviously, I remembered it."
He continued: "And then I had another person who contacted me after the race started and told me a story. But I don't want to go in since it's all second and third hand, other than to say that it's absolutely factually true. So, I don't have any doubt that we're hearing is true."
A score of women have recently come forward with allegations that Trump made unwanted sexual advances on them in the past. Trump has strongly denied the claims.
The flood of accusations came after a leaked 2005 tape showed Trump making a number of crude sexual remarks about women. He later apologized, and said the remarks were just "locker room talk."
Cuban has been a supporter for Democratic presidential nominee Hillary Clinton since he endorsed her at a Pittsburgh rally in July.
He has ripped Trump repeatedly on social media and in interviews, calling him the most "dangerous" presidential candidate he could imagine during a recent interview with Business Insider. Cuban last month offered Trump $10 million to hold a four-hour policy debate with him.
Earlier in the cycle, he was more enthralled by a potential Trump presidency, and at different points said he'd be interested in serving as either Trump's or Clinton's running mate.