Adding to the comments Depp made to the L.A. Times, our regular tipster is saying that even if he makes the fourth film, he definitely won't be back for a fifth or sixth. Given that the Pirates franchise was the only live-action property making any money for the studio, they could reach deep in their pockets and keep Depp on for #4, but they're also preparing to replace Captain Jack with a entirely new character if he refuses a fifth and sixth film.
Of course, now the speculation game begins on who will take over as the central character in the Pirates franchise. It will not be the same without Jack Sparrow, though. Whoever takes over will have such a huge presence to fill, and the movie will always be compared with the ones that Depp made.