Despite not hearing much about a sequel to the 2013 Superman Man of Steel movie, The Wrap reports sources close to WB filled them in that "Superman is a top priority for the studio and getting the character right for audiences is of tantamount importance."
The article mentions no release date or director involved with Man of Steel 2, but WB does have two untitled DC films to be released on October 5, 2018 and November 1, 2019. The report also mentions the solo Ben Affeck The Batman movie will most likely be released prior to Man of Steel 2 as well.
It was said George Miller was involved with Man of Steel 2 at one point, but Miller said while he was involved in talks with DC, regarding Man of Steel 2 it probably wasn't true.
Back a few months ago saw Henry Cavill make it known he would do Man of Steel 2 as well:
"I do believe it depends on the success of [Batman vs. Superman]," Cavill offered. "If this goes well then we can start to negotiate with Warner Bros. for a standalone Superman movie. But they've got their plans set out for other stuff and Justice Leagues and various other movies, so it's about finding the time, really. It's something that I would be very keen to do."
Zack Snyder also offered that "part of the reason we didn't announce a standalone superhero movie this time was to support some of the events of [Batman vs Superman]."
An official WB press release from almost two years ago aso saw word of more Superman movies:
And, in a massive expansion of the Studio’s DC Entertainment-branded content, Warner Bros. Pictures and New Line Cinema will release a slate of at least 10 movies—as well as stand-alone Batman and Superman films...
Zack Snyder also revealed a potential ending for their Man of Steel 2 if they didn't go with Batman Vs. Superman, which would have tied to Batman:
Originally, it was going to be a straight Superman movie. One of the ideas was that at the end of the movie, a crate of kryptonite would be delivered to Wayne Manor. That didn't happen, but once Batman was mentioned, he wouldn't go away. It couldn't be undone.
Henry Cavill will next be featured as Superman in the Justice League movie.
Here is the current DC line-up:
Ben Affleck's The Batman has yet to have a release date.