The Transformers star is being considered for the main role in the Gil Kenan-written movie, reports Variety.
The film tells the tale of a young woman who moves back home to reconnect with her brother, only to fall for his 20-foot tall neighbour, played by LaBeouf.
AngeleFine Productions has described A Giant as "Lars and the Real Girl meets Edward Scissorhands".
A Giant is expected to be released under a new title.
Lava Bear Films and the Henson Company will produce the film.
Kenan is best known as the director of the animated film Monster House and for the live-action City of Ember.
LaBeouf will not be returning to the Transformers franchise for the fourth and fifth films.