Lance Armstrong has experienced plenty of tough times, from surviving cancer to completing and winning six consecutive Tours de France.

But his endurance, and his ability to focus on cycling, are now being put to the test — by the tabloids. As he prepares for his final ride in the Tour next month, the supercyclist is trying to outrun a published rumor that his relationship with Grammy-winning girlfriend

Sheryl Crow has reached the finish line.

Armstrong adamantly denied the rumor in a recent phone call from his hometown of Austin, Tex. "Sheryl and I were in the car yesterday when somebody called us about the story," he says. "It is completely untrue."

Armstrong, 33, met Crow, 43, at a Las Vegas charity event in 2003 and says he's "mad about her. She is a great woman. We are very similar, and of course it is a challenge sometimes to work things through, but she is a true blessing in my life. I have found happiness the second time around." (Armstrong and his ex-wife, Kristin, divorced in 2003.)

With Armstrong about to retire from cycling, are there wedding plans in the future?

On that one, he says, "I always believe that it is best that the guy surprise the woman."

FYI, the Tour de France begins July 2, airing on Outdoor Life Network; Chasing Lance, FitTV's limited series profiling Armstrong and his team, premieres June 15 at 8 pm/ET.