In an interview with SFX, the MAN OF STEEL star says he’d be all for a World’s Finest movie that teamed up Superman with the Dark Knight:

I think it would be really interesting with the age-old Batman/Superman conflict,” he tells SFX, “because they are two different sides of the same coin and their methods are entirely different. And I think it would actually make for an interesting story as to why, first of all, they were going head to head and how. I think that would make a great story.

So that instantly got my mind racing with thoughts of just who would be the Batman opposite Cavill’s Superman?

I am not one of those people who has this adamant opinion that it is impossible to reconcile the more real world Christopher Nolan Batman movie universe with a universe that included super-powers and aliens. I figure if you took the idea that Batman was the first costumed hero in the world and all of the Nolan Batman movies took place before the first public appearance of Superman then nothing that happened in those Nolan films conflicts with anything that happens in other DC Universe films (including the disappointing GREEN LANTERN).

And if the Nolan films occupy the same cinematic universe then it would leave it open to have either Christian Bale’s Bruce Wayne or Joseph Gordon Levitt’s Robin Blake (who had the Batman torch passed to him at the end of THE DARK KNIGHT RISES) appear as Batman. So if Levitt is the guy it would require no real explanation since the last time we saw the character he was discovering the Batcave and embarking on his future career as The Dark Knight. If it were to be Bale then they Blake stuff could just be ignored or, if the folks behind this movie that does not exist wanted to be bold, could explain Wayne coming out of retirement and joining forces with Superman being due to Blake falling in the line of duty against some super-villain that would require the team-up.

Of course WB/DC could always go for a full reboot which would require a new actor stepping into the role of Bruce Wayne/Batman. Now many names have been bandied about since THE DARK KNIGHT RISES left movie theaters: Bradley Cooper, Armie Hammer (who was cast as Batman in the ill-fated Justice League movie that was in development a few years ago), Jake Gyllenhaal, Wes Bentley.
Most of those are good choices but the guy I think would be perfect would be Ryan Gosling. He is an incredible actor for starters and he excels at playing characters with a little darkness in them which is pretty much a pre-requisite for playing the role of Bruce Wayne/Batman. Plus he could belt out a couple Jodeci songs on set during down time.