The Oscar-nominated Silver Linings Playbook actor previously said he would be "interested" in the role after he had been reported to be in talks to star in an upcoming biopic, to be produced by JJ Abrams.
But he told Access Hollywood: "Oh my God, that's so nuts! No. I don't know anything about it."
The 38-year-old later said he has no knowledge about the part, despite JJ telling Entertainment Tonight that they have been "talking" after he sent the producer an email.
Bradley added: "I was in Manchester, doing the BBC morning show... I had no idea what [the interviewer] was talking about. I didn't even know that JJ has the rights, I had no idea."
The actor previously told the BBC that he was keen on portraying the athlete, saying: "I would be interested in that. I think he's fascinating. What a fascinating character."
Paramount Pictures and JJ Abrams' production company, Bad Robot, are planning a film about the fallen sports hero, after securing the rights to New York Times reporter Juliet Macur's forthcoming book Cycle Of Lies: The Fall Of Lance Armstrong, due out in June.
No director, writer, or start date has been set.