JJ Abrams and Paramount Pictures recently acquired a book 'Cycle Of Lies: The Fall Of Lance Armstrong' by New York Times sports writer Juliet Macur for a potential film.
Cooper, who is in the race for the best actor Oscar this year for his turn in 'Sliver Linings Playbook', finds Armstrong's character fascinating.
"I would be interested in (playing Armstrong). I think he's fascinating. What a fascinating character," Cooper told BBC News.
"I remember Matt Damon was going to do his autobiography at one point years ago. I remember thinking, that would be a great character, I'd love to play that character. I would love to do something, I think he's pretty fascinating," the 'Hangover' star said.
Armstrong accepted taking performance enhancing drugs during all his seven Tour de France wins to Oprah Winfrey recently.
The admission came after the US Anti-Doping Agency (USADA) banned Armstrong from cycling for life in August last year and stripped him of his seven Tour de France titles.
Hollywood has been interested in Armstrong's story for sometime. Two other projects were in the works but stalled late last year. One was to be based on his 2001 memoir 'It's Not About the Bike' while the other was being developed by Ed Pressman of 'Wall Street: Money Never Sleeps' fame.