Rumors have been swirling for months now that Wolverine 3 would follow the "Old Man Logan" storyline from the comic books. Recently these rumors were bolstered by Instagram pictures from Hugh Jackman showing him sporting a beard and a trucker hat, a look that bears a passing similarity to Wolverine's "Old Man Logan" appearance.
Further evidence came from confirmation that the movie will have an R-rating and a "violent western" tone and will take place in the future, all of which would fit well with the "Old Man Logan" storyline. However, a new rumor indicates that even if that storyline is borrowed from for the movie, its title will not be.
The website Gamezone is claiming inside sources have told them that Wolverine 3 will be titled Weapon X, a title that fits less with the "Old Man Logan" storyline and more with the Wolverine origin story that has already largely been covered by previous movies (including the most recent film, X-Men: Apocalypse). It's doubtful that Wolverine 3 will actually be another origin story given its setting in the future with an older Wolverine, but the Weapon X program is involved not just in Wolverine's origins, but much of his comic book history.
One of the Weapon X comic book runs tied in with the Age of Apocalypse storyline, in which Charles Xavier's son Legion goes back in time and accidentally kills him, leading to an alternate timeline in which Apocalypse takes over the earth. It's unlikely that Fox would use this storyline in full, but borrowing elements from it would allow them to tie Wolverine 3 into the recently-released X-Men: Apocalypse, making for the sort of intra-franchise synergy that they have yet to seriously tap into. Then again, after the relatively disappointing performance of X-Men: Apocalypse, Fox might not be too keen to keep drawing from that well.
Another possible source of inspiration for Wolverine 3 is the Weapon X series that ran from 2002 to 2004 and featured, among other plot elements, the introduction of X-23, a female clone of Wolverine. X-23 has been rumored for inclusion in Wolverine 3, so borrowing those plot elements would make sense. There were also additional Weapon X series launched in 2005 and 2009, and the movie could borrow from either or both of those as well.
The Weapon X title is at this point just an unsubstantiated rumor, and a dubious one at that. The title is most closely associated with Wolverine's origin, and it would seem odd for Fox to potentially confuse audiences into thinking they would be subjected to yet another Wolverine origin story. Nevertheless, even if that title ends up being used, the future setting and older Wolverine seem like sure things at this point, so an actual origin story is very unlikely. It would be surprising if at least some elements of the "Old Man Logan" storyline are not used, but given this rumor it's entirely possible they'll be mixed up with elements of one or more of the Weapon X storylines as well.
X-Men: Apocalypse is now playing in theaters. Wolverine 3 opens in U.S. theaters on March 3rd, 2017, followed by unannounced X-Men films on October 6th, 2017 (possibly Gambit), March 2nd, 2018 (possibly Deadpool 2), and June 29th, 2018 (possibly New Mutants). X-Force is also in development.