Update: September 16, 2015
Rumor: Brainiac is JUSTICE LEAGUE Foe; MAN OF STEEL 2 Dead
While Man of Steel looks like a success to you - $290 million domestic! $660 million global! - it fell short of expectations for Warner Bros. Just like Amazing Spider-Man 2, which earned $700 million global but still killed that franchise, Man of Steel is an underperformer. It was supposed to hit a billion. It was that underperformance that led Warner Bros to scrap sequel plans and instead shove Batman into the next Superman movie, giving us Batman v Superman: Dawn of Justice rather than Man of Steel 2. According to Birth.Movies.Death, rumors have been flying that Superman's solo movies are essentially dead, that WB doesn't want to give the Big Boy Scout another movie until they have established the entire DC Movieverse.
Over at Heroic Hollywood El Mayimbe is more upbeat. He thinks that while Man of Steel 2 is on hold it isn't exactly dead, and he's even found out about the story Zack Snyder and David Goyer pitched after Man of Steel (but before WB changed their plans to BvS). According to Mayimbe the sequel would see Brainiac arriving on Earth, looking not for Superman but his cousin, Kara Zor-El, Supergirl. She was actually set up in a prequel comic that DC released that we were told was canon; in it Kara was a member of the Kryptonian 'Explorer's Guild,' who had been tasked with terraforming worlds. That means she might have been out in space when the cataclysm befell Krypton.
According to HH Man of Steel 2 was always going to be a split-hero affair, but in this case it was going to spend a lot of time on Supergirl. She would get about half the screen time, and over the course of the film Brainiac would create Bizarro to hunt her down. That means Man of Steel 2 would have Supergirl, Brainiac and Bizarro - quite the Silver Age line-up.
BMD trust El Mayimbe's sources, but the site suspects that a lot of this stuff is scrapped now, especially as every whisper the site hears about Justice League contains the word 'Brainiac.' BMD suspects elements of this story were cannibalized for the eventual team-up as well as BvS, whose main physical threat is a cross between traditional Bizarro and another well-known Superman villain. Plus, if the movie division had serious plans for Supergirl the site can't imagine they would have allowed the new Supergirl TV series to take off (the movie guys removed Suicide Squad from the toys Arrow could play with in advance of the film).
There will be another solo Superman movie some day, and it may even be in the same continuity as Man of Steel, but BMD is guessing that day is long off, and whatever plans and ideas Snyder had in 2013 will be changed and evolved when the film hits the screen.
Rumor: Brainiac Will Be the Villain in Justice League; Man of Steel 2 Put on Hold