(Marvel)
If you're the type who follows superhero movie news, you'll know that Marvel doesn't have the film rights to all of the characters that appear in its comics. In fact, two of the biggest parts of its comic book universe — the Fantastic Four and the X-Men — are licensed by 20th Century Fox, and all the characters with ties to them are contractually forbidden from appearing in movies made by Marvel Studios.
This is why popular characters like Wolverine won't ever appear in an "Avengers" film, and why the news that Spider-Man has joined the Marvel Cinematic Universe was such a big deal. But since Fox has the rights to both the Fantastic Four and the X-Men (both huge properties with loads of characters and worlds unto themselves), it stands to reason that they would build their own mini-Marvel Cinematic Universe, since that sort of thing is so hot right now — and also because screenwriter/producer Simon Kinberg has worked on both rebooted franchises (there's also a comic book precedent).
(Alan Markfield/20th Century Fox)
In a recent video Q&A with Yahoo Movies, "X-Men: Apocalypse" director Bryan Singer answered a number of fan questions — and one of them was about the presumed crossover.
"That would be a natural match-up because they’re both ensemble films and there is a natural mechanism by which to do it," said Singer. "It deals with time — that’s all I’m going to say.”
Singer didn't say anything else about the potential project, but based on the films as they stand now, time travel is probably the only way to bring both casts together in a way that makes sense — it was used in "Days of Future Past" to effectively reboot the "X-Men" movies and turn them into period pieces ("Apocalypse" is set in the 1980s), while "Fantastic Four" looks like it's set in the present day. So time travel is a nice convenience, and probably a necessity from a plot perspective.
(20th Century Fox)
Singer also makes sure to hedge his bets when talking about the potential crossover, noting that it's important to make sure both movies do well before getting too deep into speculation about a potential crossover.
The whole Q & A is worth a watch — Singer spends most of it answering questions about the recently-released "Rogue Cut" of "X-Men: Days of Future Past", but also drops a bunch of other great "X-Men" tidbits — like briefly teasing that "Apocalypse" might have feature the X-Men in their iconic comic book costumes at some point.