According to Empire Magazine (and credit to the folks over at Obsessed With Film for finding it), there is potential for not only an X-Men 4, but an X-Men 5. Franchise producer Lauren Shuler-Donner said the following:
"We took the treatment to Fox and they love it… And X4 leads into X5."
So, for the sake of discussion let's take that as truth. Now, who will helm it? Screen Rant seems to believe it will undoubtedly be Bryan Singer, which isn't too bad of an assumption. Two years ago, Singer was quoted saying that he was "eternally intertwined with X-Men" after kicking off the last decade of superhero cinema with X-Men in 2000 and X2 in 2003. In fact, if it hadn't been for some pretty lame scheduling conflicts regarding Warner Bros. Jack the Giant Killer, he would not have dropped out of X-Men: First Class and the anticipated prequel would be his next directorial effort (he remains a producer of the project, though).
If it does move forward, X4 (and X5, I guess) will have a hefty price tag, specifically for the talent alone, including Hugh Jackman, Halle Berry, James Marsden, Anna Paquin, Patrick Stewart, Ian McKellen, just to name a few (and all despite that fact that two of the characters played those two of those six names perished in the best-forgotten X-Men: The Last Stand). The sources claim that the big-budget undertaking could entice Fox to film the next two chapters in the mutant saga back-to-back, much like Disney's first two Pirates of the Caribbean sequels.
But hey, this is a good thing, right? I mean, it's not like right now there aren't already two X-Men movies in production (The Wolverine and First Class) on top of the countless other superhero films releasing over the next couple years. Honestly, it might be safe to assume that this all just one big masterminded plan of Hugh Jackman's. Maybe he finally came to the realization that Wolverine is pretty much the only thing of note he'll do for the rest of his career, so, you know, he's just going to stretch that out for as long as possible.