According to a story from Journal de Montreal, production offices have been set up to open in November 2016 for shooting to begin in 2017 with Singer at the helm. That film would likely take the July 13th 2018 slot that has already been set aside. The story quotes Mel Studios president who says, "It was a miracle that we managed to attract a movie X-Men in Montreal in 2013. To convince Fox to return for a second and now a third is simply amazing".
Take all of this with a grain of salt until Fox makes some kind of announcement, but keep in mind that Singer's next project is supposed to be an adaptation of 20,000 Leagues Under the Sea. Plus, with the X-Men franchise evolving and stories suggesting it is the end of Singer's run, attaching him as director of another film seems premature. Probably best to file all of this as a rumor for now.