The movie - based on the autobiography Kyle - will be produced by Cooper's March 1 company, The Hollywood Reporter said.
Jason Dean Hall is writing a script based on the book - which has the complete title 'American Sniper: The Autobiography of the Most Lethal Sniper in US Military History' - which reveals how Kyle recorded the highest number of sniper kills for an American and has been praised for its honest first-person account of a man who shoots from far and close distances.
The book also features passages from Kyle's wife who reflects on how her husband's passion switched from her to war and the SEALS (United States Navy's Sea, Air and Land Teams).