Broadway star Lily Rabe has already signed on to play Pickford in the film, produced by Jennifer DeLia and Al Pacino's daughter Julie Pacino.
Rabe is perhaps best known to television audiences for her role as ghost Nora Montgomery on season one of American Horror Story.
According to Forbes, DeLia and Pacino are currently eyeing Law to play Fairbanks, who was one of Pickford's three husbands during her tumultuous career.
Together, they formed the United Artists studio with Charlie Chaplin and director DW Griffiths in 1919.
Josh Fagin, best known for last year's Warrior, is adapting the film's script from writer Eileen Whitfield's Pickford: The Woman Who Made Hollywood.
The film starts production next year.
Law will next star opposite Richard E Grant in the upcoming comedy Dom Hemingway.