DC is owned by Warner, and I believe Warner has kept all its licences in-house, rather than farm them out like Marvel used to do.
Marvel is owned by Disney. It has its own studio, Marvel Studios, that is responsible for all the "Marvel Cinematic Universe" films (Iron Man through to The Avengers). Aside from those, there are some Marvel characters that Marvel does not currently hold the rights to (X-Men = Fox, Spider-Man = Columbia/Sony).
So I don't see how any other studios could jump in with other DC/Marvel characters.
Red was a DC property that was released by Summit Entertainment but that was due to WB passing the project and allowing the producer to take it elsewhere.
Marvel Studios was set up before Disney bought Marvel, Marvel still makes some money from films like X-Men and Spider-Man but ultimately have no control over them, Sony's contract with Spider-Man is that as long as they keep making Spider-Man films, they keep the film rights.
DC films tend to be produced with other producers like Legendary Pictures who did the Batman films and Superman Returns, I agree they need someone to guide a DC Film Universe but I'm not sure if Christopher Nolan is the right person.