There's been no word on whether Abrams will direct, no casting details, or mooted start date for the film.
'I WOULD BE INTERESTED IN THAT'
Cooper, who is up for an Academy Award for his role in Silver Linings Playbook, told BBC News he would "love" to play Armstrong in the planned biopic.
"I would be interested in that," he told the website.
"I think he's fascinating. What a fascinating character."
Cooper added: "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."
Cooper said he had not been in discussions with the studio over the role.
Damon, Jake Gyllenhaal, Michael Fassbender and Christian Bale are said to be other names that have been linked to the role.
Another movie based on Armstrong's life, with Gyllenhaal tipped to star in the lead role, was dropped by Sony after the sportsman's fall from grace.
Meanwhile, Armstrong's ex Sheryl Crow has weighed in on her ex-fiancé's recent doping confession.
Crow, 50, who dated the cyclist from 2003 to 2006, appeared on Entertainment Tonight this week, and briefly discussed (albeit very generically) the scandal surrounding her ex.
"I know how hard he worked to win those titles, and you know, it was hard to watch," Crow said adding that she had watched "bits and pieces" of his interview with Oprah.
"I felt bad. I felt bad for him, I felt bad for his family, and I kinda felt like the rest of America. He is a hero that we watched and looked up to and admire," she elaborated.
"I think that honesty is always the best bet and that the truth will set you free," she added. "To carry a weight like that around would be devastating in the long run...I always contend that the truth is the best way to go."
Check out Crow's interview below:
Armstrong's close pal (and fellow Texan) Matthew McConaughey, recently admitted he was initially "pissed of" that the shamed sportsman had been lying about doping.
"My first reaction was I was pissed off," he told MTV News.
"I was mad. I then got kind of sad for him. First off, I had a part of me that took it kind of personally, which I think a lot of people have."
"For him, it was impersonal because he was living a lie," McConaughey added. "It was a whole unanimous facade he had to carry around."
He continued: "What I realised is that those of us that took that personally, like, 'Oh, he lied to me', it's not true.
"What I mean by this is, what was he supposed to do? Call me to the side and go, 'Hey man, I did it but don't tell anybody'. Then I would have really had a reason to be pissed off at him, going, 'You want me to walk around holding this?'"
McConaughey went on to explain: "Where I am now is I've put myself out of the way and I am happy for this guy, who has now chosen to reenter this new chapter of his life a truly free man. And the weight he had on his shoulders, without the boogieman under the bed, the skeleton in the closet that he's carried for 14 years. Fourteen years he lied and carried the lie with him."
Check out his interview below:
FAST GOSSIP
And finally...
* Aretha Franklin admits she "laughed" at Beyoncé lip-synching controversy.
* Kate Middleton portrait artist hits back following "vicious" criticism.
* Adam Lambert, Cyndi Lauper to record Mad World duet?
* Angelina Jolie opens up about how her kids keep her grounded.
* "I'm sure they're going to make a really cool movie" - Shia LaBeouf on Transformers 4, which he won't be starring in.
* Mila Kunis accused stalker gets rehab, protection order.
* Those rumours about Demi Moore dating Lindsay Lohan's ex re-surface.
* "There comes a time when you're just like, 'screw you'" - LeAnn Rimes talks ongoing feud with Brandi Glanville.
* Harry Styles and Taylor Swift back on again?
* Is Adele wearing her baby son's name around her neck?
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