While X-Men: Days of Future Past teased an epic continuation, X-Men: Apocalypse was one of the bigger letdowns of 2016. Even so, producer Simon Kinberg started working on a script for the sequel last summer, saying that the movie will take place in the "˜90's. As far as the plot is concerned, Bryan Singer (who won't return to the director's chair) teased the villain Proteus (he is Moira MacTaggert's son), while X-Men: Apocalypse clearly revealed that we’re heading toward a new (and, hopefully, better) adaptation of the Dark Phoenix Saga.
This being said, Production Weekly and My Entertainment World may have discovered the title (or, at least, the working title) for the next X-Men installment (which hasn't found a director just yet): X-Men: Supernova.
Of course, at this point everybody can believe that the Dark Phoenix Saga will indeed be adapted (unless Simon Kinberg decided to draw from the X-Men: Supernova title, with Rogue as the leader of the team - to be noted, there is currently no Rogue in the rebooted X-Men universe).
Nonetheless, this should be taken with a grain of salt, since My Entertainment World also notes that X-Men: Supernova will start shooting this May. This is hard to believe, given the fact that we've heard nothing about this sequel until now (as said, a director hasn’t even been announced).
We do know, however, that James McAvoy will return as Professor X, along with younger cast members Alexandra Shipp, Tye Sheridan, and Sophie Turner (Storm, Cyclops, and Jean Grey), who had signed multi-picture deals when announced for X-Men: Apocalypse. On the other hand, it’s uncertain whether Jennifer Lawrence and Michael Fassbender will return.
For the moment, there is no scheduled release date for the next X-Men movie.