A while back it was rumored Matthew Vaughn was up to direct Man of Steel 2, and now it is at least confirmed Matthew Vaughn is interested in directing the sequel to Zack Snyder's 2013 Superman reboot.
“I know Matthew’s [Vaughn] a big Superman fan. Would I like to… I don’t know. I mean I’m not sure. I think Matthew’s looking at it from a directing point of view. I have no idea what’s happening there.”
Jane Goldman was also asked if she would like to write Man of Steel 2 and thinks there might already be a script:
“I’m not sure. There might already be a script for it. I think so… I’m not certain actually but it’s complicated with a character with that kind of history. Obviously X-Men have an equally complicated [history]… but Superman feels a lot more recent. He’s been brought to life in a new iteration – he means a lot to a lot of people and maybe there are other people with more a connection with Superman… but who knows.”
Back in 2010, saw Matthew Vaughn comment on doing a Superman movie:
“I think that’s the one thing not to do with Superman, trying to do the serious The Dark Knight version. Superman is about color and fun, or it should be, for me," Vaughn told MTV back in 2010.
Man of Steel 2 hasn't been officially announced by WB, but Henry Cavill's manager did confirm Man of Steel 2 is in development and there is also speculation Dwayne Johnson's Black Adam may appear in Man of Steel 2 to battle Henry Cavill's Superman.
WB did just announce two release dates for untitled DCEU movies in 2020, hopefully one is for Man of Steel 2!
Current rumors surrounding Man of Steel 2 are stating it may feature both Brainiac and Supergirl.