Kyle's book, American Sniper, was already in talks to become a movie prior to Kyle's death.
Cooper, who also will co-produce the proposed movie, spent Thursday meeting with the other producers and the movie's scriptwriter, he told NPR's Fresh Air.
Speaking with NPR host Terry Gross, Cooper said he was exploring ...
...how we can speed up the process and really try to make this movie. His story, first of all, needs to be told. And it's also relevant on two fronts. One, gun control, and two, the need to address the many soldiers that are coming back with post-traumatic stress disorder.
Kyle, 39, was allegedly shot in the back along with his friend, Chad Littlefield, 35, by Eddie Ray Routh, 25, at a Dallas shooting range. Routh, a former Marine, is reported to be battling PTSD.
The most lethal sniper in U.S. military history, Kyle had between 160 and 255 kills during his four tours in Iraq.
In a sad twist, Cooper was researching the movie — meeting with PTSD-afflicted veterans — when he heard the news of Kyle's death. Cooper said:
Medicine has evolved to such a state that more soldiers are coming back and they're going to assimilate into the culture, and if we don't address the mental state along with the physical state, it's going to be a problem.
The movie will be written by Jason Dean Hall, who last wrote the 2009 Ashton Kutcher comedy Spread.