2) Edgar Wright
Edgar Wright obviously came very close to directing a superhero movie with Ant-Man, but creative differences with Marvel Studios saw the British director walk away from the project. Assuming Fox can back off and give the man responsible for gems like Shaun of the Dead and Scott Pilgrim vs. The World the space he needs, he could very well come up with an X-Men movie which takes this franchise in an exciting new direction.
That would no doubt particularly be the case in terms of visuals, while Wright’s well-known love of silver age comic books (which heavily influenced his Ant-Man screenplay) could bring a classic sensibility to the franchise which it’s arguably always been missing. If they can talk him into it, nabbing Wright would be a massive victory for Fox, and fans would definitely get on board with him being at the helm, something the studio could do with after the mixed reaction to X-Men: Apocalypse.