The screenplay was adapted from Kenneth Slawenski's biography, J.D. Salinger: A Life.
Black Label Media is financing, with Molly Smith, Trent Luckinbill and Thad Luckinbill producing alongside Strong, Bruce Cohen and Jason Shuman.
Bloom will introduce the project to foreign buyers at the upcoming Toronto International Film Festival.
"The Catcher in the Rye is a classic coming-of-age story, which continues to make a significant impression six generations later. The world has long been fascinated with J.D. Salinger, who the talented Nicholas Hoult will bring to life, in this enigmatic role," Bloom's Alex Walton said in a statement Monday.