Trump and Armstrong went on "several" dates, says a source

So much for Lance Armstrong’s Tour de Trump. The cycling champ and Ivanka Trump went on “several dates,” sources tells PEOPLE, but the relationship never got out of first gear.

Trump, 24, is vice president of development and acquisitions for the Trump Organization. She and Armstrong, 35, met at a charity event in Los Angeles a few months ago when she was in town filming dad Donald’s NBC reality show The Apprentice, according to a source.

Armstrong’s rep says there was no romance, and a pal says Trump hasn’t seen the seven-time Tour de France winner in a month.

Trump herself told PEOPLE on Monday, “I have tremendous respect for Lance and all he has accomplished. That said, we are just friends.”

Armstrong has three children from his first marriage. He was also engaged to singer Sheryl Crow, although the couple split in February after two years of dating.