The writer is behind famous children's stories including Oh, The Places You'll Go!, Horton Hears a Who! and The Cat in the Hat.
Universal and Illumination Entertainment are financing the film, which is not expected to feature any animation. The former made Geisel's The Grinch Who Stole Christmas and adapted The Cat in the Hat, with Mike Myers in the lead role.
In Treatment writer Keith Bunin will pen the screenplay, with Depp potentially taking the title role.
Depp has been attached to several projects, including a remake of the 1970s television series The Night Stalker.
The actor will next be seen in Dark Shadows and the troubled big-screen adaptation of the series Lone Ranger, where he will play Tonto.
Universal gave the adaptation the go-ahead after Depp and Pirates of the Caribbean director Gore Verbinski agreed to lower their fees.
> Johnny Depp is Hollywood's highest earner with $350m from 'Pirates'
See pictures of Depp on the Dark Shadows set below: