While we know precious little about Hugh Jackman's third and final go around as Wolverine—outside of him looking like a livery driver—there are certain puzzle pieces that we can assemble in a certain way to potentially know a bit more about the film. Again, this is all rampant speculation until we hear otherwise, but there's some interesting stuff to be found in here.
Comic Book Resources (link below) has some interesting theories surrounding Wolvy's appearance in X-Men: Apocalypse and how that post-credits sequence may have been more set-up for this film, allegedly titled Weapon X, rather than future X-Men sequels.
The final scene in "Apocalypse" wasn't focused on the mutants, Professor X, or even Magneto -- it took us back to Alkali Lake where someone with a briefcase stole a vial of Wolverine's DNA. The briefcase was lined with a few other DNA samples and had the name Essex written on it. In the comics, the Essex Corp. was owned by Mr. Sinister, a known villain of the X-Men with a penchant for cloning. His origins were revealed in "The Further Adventures of Cyclops and Phoenix" in which Scott Summers and Jean Grey traveled back to Victorian London., where they discovered Apocalypse had imbued scientist Nathaniel Essex with mutant abilities, particularly that of not aging. Essex also tried to clone numerous X-Men in the comics, including Jean and Cyclops.
British actor Richard E. Grantwas recently cast in "Wolverine 3" as a mad scientist type, could he be playing Dr. Nathaniel Essex AKA Mr. Sinister? If Mr. Sinister is going to play "Wolverine 3's" villain and he has Wolverine's DNA via that post-credit scene, could he be the man responsible for creating Logan's clone X-23? So far no one has been cast as Laura Kinney/X-23 in "Wolverine 3," but a casting call was recently put out for a young woman who, like X-23, was raised in captivity.
From the moment Grant was cast, my hope was that they'd give him something worthwhile to do, meaning I'm a huge fan of this theory that he's playing Mr. Sinister. That would be fantastic! Similarly, they've been hinting at X-23's involvement with this film for a while, so I don't doubt she's going to play a substantial role in this film, likely setting her up to take over things once Jackman hangs it up. Interesting stuff, we'll have to wait and see how this all plays out.