Heath, who was found dead in his hotel room earlier this week, was just six weeks away from wrapping 'The Imaginarium of Doctor Parnassus'.
Director Terry Gilliam is keen for Johnny to shoot the remaining scenes as he thinks the 'Pirates of the Caribbean' star would be the perfect replacement.
A source said: "There is a point in the film when Heath falls through a magic mirror. He could change into another character after that and that is where Johnny would come in.
"It's a weird, fantasy, time-travel movie so Heath's character could easily change appearance. It would be a poignant moment. Johnny's not working at the moment so everyone is praying he will do it."
Just three days before his untimely death, Heath reportedly had a furious row with producers on the London set of the movie after they refused to reshoot a scene.
Heath, who was known in the industry to be a perfectionist, was said to be unhappy with the scene and was furious when they wouldn't change it.
TAGS: Movies Johnny DeppHeath Ledger