According to The Hollywood Reporter, the 77-year-old actor will play a man who shares unbelievable tales about dragons to his logging community, if he secures the role.
A fishing village was the setting for the original 1977 movie, which told the story of a boy named Pete and his relationship with Elliot the dragon.
David Lowery's remake will be live-action, using CGI effects to bring the dragon to life instead of animation.
Oakes Fegley - who has starred in 'Boardwalk Empire' - is due to play Pete, while Oona Laurence is set to take the role of a mill owner's daughter.
Redford recently starred in 'Captain America: The Winter Soldier' and is currently working on 'A Walk in the Woods'.