The British actor has approached producers about depicting the late Hallelujah hitmaker once he completes the last two movies in the vampire franchise.
But Pattinson, who sang on the Twilight soundtrack, will have to impress with his musicianship if he wants to land the coveted role.
Producer Michelle Sy says, "I've met actors who are keen on the part and Robert was one... The actor must be able to play music and sing, or at least make it believable he can do that."
The 24 year old has already received a vote of confidence from Mary Guibert, Buckley's mother, amid reports actors including James Franco and James Marsden are also vying for the part.
Guibert says, "Robert is a fine young actor. I'm flattered he's been linked to the project. When the times comes we'll give everybody an opportunity to be seen and heard."
Buckley drowned in Memphis, Tennessee in 1997 when he was just 30 years old.