In the Warner Bros origin story, an orphan is taken to Neverland and leads a rebellion against the pirates, reports Deadline.
Bardem is said to have agreed to play the villainous Blackbeard in the film, which is also expected to feature Captain Hook.
Pride & Prejudice and Atonement director Joe Wright is reportedly in talks to direct the movie.
Meanwhile, Ice Age: Continental Drift's Jason Fuchs has written the script and Greg Berlanti is on board as producer.
Both Disney and Sony are also believed to be working Peter Pan movies.
Disney's Peter and the Starcatchers will be directed by The Hunger Games' Gary Ross, while Channing Tatum is involved in Sony's project.