The newspaper said Depp could possibly also play the "Cat in the Hat" scribe, but has not yet signed on to do so.
Illumination Entertainment and Infinitum Nihil are developing the bio-picture, and Universal Pictures has agreed to distribute it.
Depp frequently works on projects associated with classic children's tales. He played the Mad Hatter in "Alice in Wonderland," "Peter Pan" author J.M. Barrie in "Finding Neverland," Willy Wonka in "Charlie and the Chocolate Factory" and Capt. Jack Sparrow in "The Pirates of the Caribbean" movies, which were based on a popular Disney theme-park attraction.