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The seven-time Tour de France champ has been quietly dating Burch for months, according to sources.
"They are very much a couple," says R. Couri Hay, a friend of the designer's.
Reps would not comment on the relationship but Burch – whom Armstrong contacted, says a friend, after reading her profile in Vanity Fair – has already visited him in Texas several times.
Most recently, the couple cozied up at Houston's Hotel Derek on March 6, where they drank margaritas before heading off to a reception in Burch's honor. (Also in town at the time was Armstrong's ex-fiancée Sheryl Crow, who bears a striking resemblance to Burch. The longtime couple called it quits in February 2006.)
Another source tells PEOPLE of Armstrong and Burch: "I can't say whether it's long-term, but they're having a great time."
