The Blind Side director is in talks for the film - documenting the true story of the making of the original Walt Disney musical - reports Deadline.
The film will follow the 14 years Disney spent convincing Australian author PL Travers to allow him to adapt her novel into a movie.
The result was the 1964 musical classic starring Julie Andrews, Dick Van Dyke and David Tomlinson, the latter of whom played the titular Mr Banks.
Tom Hanks has been rumoured to be in the running for the role of Disney, with Oscar winner Meryl Streep mentioned for Travers.
Travers was deeply attached to her novel, and apparently so hated the animated sections of the Mary Poppins film that she refused to sell any more of her work to Disney.
Hancock was recently announced to be directing John Grisham adaptation The Partner.
Saving Mr Banks was featured on last year's 'Black List' of unproduced screenplays.