The Thor director is reportedly having talks with Paramount Pictures to replace the outgoing Jack Bender, who quit production last week due to scheduling conflicts, reports Variety.
The website claims that if Branagh signs a deal soon, the project will remain a top priority for the studio.
The currently untitled project will follow the character of Jack Ryan, created by Tom Clancy.
Chris Pine has signed up for the action movie as Ryan, who has previously been played by Harrison Ford, Ben Affleck and Alec Baldwin.
Production on the film was previously delayed by script issues and Pine's commitment to the Star Trek follow-up. Filming is still expected to begin once JJ Abrams's sci-fi sequel is completed.
Kenneth Branagh was nominated for 'Best Supporting Actor' for his role in My Week with Marilyn at this year's Oscars, but lost out to Christopher Plummer.