The Hunger Games screenwriter is reworking the script for the long-gestating project, reports Deadline.
He will replace Phil Alden Robinson (Field of Dreams) on the Universal Pictures biopic of the Rat Pack musician.
The singer's daughter Tina Sinatra is attached to produce the film with Scott Rudin and Mandalay's Peter Guber and Cathy Schulman.
Guber and Schulman previously acquired the rights to Sinatra's back catalogue from Frank Sinatra Enterprises.
Scorsese is currently directing the Leonardo DiCaprio-starring The Wolf of Wall Street.
Ray has also worked on The Secret in Their Eyes (which he will also direct), an untitled JJ Abrams project, The Thin Man, Pan and the recently completed Captain Phillips.
An actor is yet to be cast in the leading role.
Watch Sinatra perform 'That's Life' below: