It is presumed that "The Wolverine 2" (they no longer count "X-Men Origins: Wolverine") might be the final run for Hugh Jackman as the iconic mutant. The prevailing presumption is that the release of the "Death Of Wolverine" series in the comic book is not exactly a coincidence.

Indeed, the primary speculation is that the Death of Wolverine is a sneaky way to let Jackman out of the franchise. But there is also another option for the possible plot of the next movie since director James Mangold  has already mentioned that the plot would be based on a comic book story arc. It is also scheduled for a March 3, 2017 release date, less than a year after "X-Men: Apocalypse."

There is definitely a connection between the two movies since they will be filled one after the other. Thus, there is also a possibility that Wolverine may not die and they will follow the Old Man Logan plot.

Hugh Jackman has actually teased this:

From Screen Rant: "A few years, not that far. So, it's not that long after X-Men 3 finishes, long enough so that you see him-and you've probably seen the pictures of me with a really long ass beard and the long hair. Right. So, obviously long enough for that, and long enough to feel that he's settled into this kind of rut that he's in. Essentially, he's doing his best to stop himself from inflicting more damage and pain on everyone around him. I didn't answer the second part about the older. I think that would be fascinating, and I think that I can't really answer that question because you're onto something."

As of now, Death of Wolverine #2 has recently been released in which Wolverine will be traveling to Madripoor, a fictional island that was supposed to be located off the coast of Singapore. It has been a historic site for Wolverine and the implication is that The Hand is involved.

Considering the Japan-centric storyline in the previous movie, a visit to Madripoor might be a logical follow up but everything is up to speculation at this point.