The shamed seven-time Tour De France champion has dominated headlines of late after finally admitting to talk show titan Oprah Winfrey that he had relied on banned substances to help him win races throughout his career.
Abrams managed to secure the rights to turn the athlete's fall from grace into a new film, and Cooper recently admitted that given the chance, he would love to tackle the part.
He told the BBC, "I would be interested in that. I think he's fascinating. What a fascinating character."
Cooper has since contacted Abrams directly to discuss the biopic in more detail, and now the Star Trek director has confirmed the Oscar nominee is being considered for the lead role.
He tells U.S. news show Entertainment Tonight, "(Cooper) sent me an email and we've been talking."
Abrams and partners at his production company Bad Robot bought the rights to Juliet Macur's forthcoming book Cycle Of Lies: The Fall Of Lance Armstrong earlier this month (Jan13).
The cyclist, who spent years denying doping allegations, was stripped of his 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.