Here’s the short-list according to Deadline:
Fredrik Bond: Director of The Necessary Death Of Charlie Countryman which was first shown at the Sundance Film Festival earlier this year. It stars Shia LaBeouf, Mads Mikkelsen, and Rupert Grint, and Bond has apparently caught the eye of producer Jerry Bruchkeimer which may give him an advantage.
Joachim Rønning and Espen Sandberg: The duo come from Norway and are familiar with the high seas having recently directed Kon-Tiki, a film that tells the story of legendary explorer Thor Heyerdal’s epic 4,300 miles crossing of the Pacific on a balsa wood raft in 1947. They seem to be the top contenders, and it would mark their first big studio movie after the supernatural action project Spectral didn’t work out for them at Legendary Pictures.
Rupert Sanders: The director of Snow White and the Huntsman has some buzz surrounding him and would be the safest choice for Disney. He’s already got a successful summer movie on his resume.
Jeff Nathanson, writer of Rush Hour 2 and 3, Catch Me If You Can, The Terminal, and more recently Tower Heist, was brought on to work on the script earlier this year. Previously Johnny Depp said whether he returns for another film “boils down to story, script and filmmaker” so the actor may have some input on who helms the next movie.