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Shooting on the Terry Gilliam-directed movie was put on hold when Ledger was found dead in his Manhattan apartment on Tuesday.
According to The Sun, the project was less than two months from completion and Gilliam now wants to film the rest of it with Depp in the lead role.
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."
Oscar nominee Daniel Day-Lewis paid an emotional tribute to Ledger during an appearance on Oprah Winfrey's chatshow yesterday.
> Heath Ledger - Life In Pictures
