According to director of "The Death of Superman Lives" Jon Schnepp, who appeared on the YouTube show "PopCorn Talk," stated that George Miller, the director of the recent smash hit Mad Max: Fury Road, will reportedly be the director of Man of Steel 2, the true sequel to Man of Steel.
George Miller. He's doing Man of Steel 2. Obviously, Zack Snyder is doing Justice League 1 and 2. We already got James Wan doing Aquaman. Waterman I think they should change the title, but yeah I think George Miller is a perfect choice to do Man of Steel 2, he's going to bring so much to it.
Check out Schnepp revealing the info for yourself. It starts at 55:24.
Man of Steel 2 is not in the line-up for upcoming DC films though, which are slated up until 2020. Obviously, it's possible they could fit it in somewhere, but as of right now, there's no news from Warner Brothers to lend his statement any credibility, but we will keep you updated as more develops.