The 25-year-old had made no secret of his desire to play the Hallelujah singer, according to MTV News.
But actor Reeve Carney has beat of competition from Pattinson to be cast as Jeff in the forthcoming biopic.
Despite been relatively unknown, the Reeve, 28, recently appeared in the Broadway show Spider-Man: Turn Off the Dark.
The as-yet-untitled film has been approved by Buckley's mother Mary Guibert, Collider reports.
In a statement, she said: 'We are over the moon that Reeve has agreed to take on this challenging role. I've seen him perform several times.
'He's been getting ready for this all his life. It certainly doesn't hurt that he looks so much like Jeff.'