In an interview, the people at Marvel basically said that they are currently happy with having Fox handle the X-Men universe as its own, separate thing. And honestly, I'm kind of in agreement with them. On the Marvel Cinematic side; Ironman and Hulk have finished their movie runs, Thor and Captain America about to finish theirs, we're about to get into Avengers 2, and so much has all ready been done. I know there is still a lot more to do, but if Marvel takes over now, it would have to be a reboot for the sake of consistency, and that's a LOT to really catch up on and properly set up. About as much as Fox has all ready done, if not more.
Also, maybe it's just me, but it seems like the X-Men really need their own universe. On the one hand, we have a universe where heroes are, for the most part, loved and admired (Spider-Man, Avengers). But on the other hand, we have a universe where heroes and potential heroes are outcasts and the subject of prejudice (X-Men). Not that mixing these two universes could never be done, and there are plenty of crossover stories to draw from, but I think this proves my point. A lot of catching up to do and probably some backpedaling. A lot of people say it's easy, to "just have the character randomly show up and do their thing", but that's not how Cinematic Marvel does things. That only happens in the bonus footage after the movie is over; and in the follow up movies, they properly set things.
I think Jackman himself said he can't do this forever, and I'm guessing he might use X-Men Apocalypse and Wolverine 3 to close out his run as Wolverine.
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Sounds like he'd be game. It would be cool, but again 20th Century Fox has no reason to partner with Marvel Studios.
I've learned to take what actors say about doing these roles with a little grain of salt. In one interview, Robert Downey Jr. made it sound like he was done doing Iron Man, save for the Avengers movies. But then, in a more recent interview, he said he'd love to return for a 4th, 5th, or however many movies Marvel wants to make as long as they'll make money and he gets paid for it. Despite being afraid of getting too use to playing one specific character or character type, a lot of actors are not as picky as they once were. As long as they've got a pay check and their personal boundaries are respected, they'll take just about any kind of role. In fact, you kind of proved my point by your own example. Jackman said he doesn't want to do Wolverine forever, and yet he'd love to be in a crossover with the Avengers. Can't be in a crossover if you've dropped out for good.