The Twilight star is apparently eager to beat 127 Hours actor James Franco to the role, seeing it as the part that could put him in line for an Oscar nomination.
“Rob is obsessed with this project and is doing everything he can to land the part," a source told the Daily Express. “He has already told his business team this is his passion and they agree it could be the film that makes him a legitimate Oscar contender."
Producer Michelle Sy admitted that she has met with Pattinson about playing Buckley - who drowned in 1997 at the age of 30 - noting that the actor chosen will be required to play and sing Buckley's songs.
Mary Guibert, Buckley's mother, said of Pattinson: "Robert is a fine young actor. I'm flattered he's been linked to this project. When the time comes we'll give everybody an opportunity to be seen and heard."
Buckley's 1994 debut album Grace has sold more than 2 million copies worldwide and three compilation records have been released since his death.
He experienced a surge in popularity in 2008 when his version of Leonard Cohen's 'Hallelujah' made it to number two in the UK charts at the time of X Factor winner Alexandra Burke's release of the same track.