The sports star made headlines last week (ends20Jan13) after telling talk show host Oprah Winfrey he had spent years taking banned substances to help him win cycling races.
Director J.J. Abrams has secured the rights to turn Armstrong's fall from grace into a new movie, and Cooper admits he would be open to playing the lead role.
He tells the BBC, ""I would be interested in that. I think he's fascinating. What a fascinating character.""
Abrams and partners at his production company Bad Robot have bought the rights to Juliet Macur's forthcoming book Cycle Of Lies: The Fall Of Lance Armstrong.
The cyclist, who spent years denying doping allegations, was stripped of his seven Tour De France titles by officials at the United States Anti-Doping Agency, and he was also ordered to return the bronze medal he won at the Sydney Olympic Games in 2000.