I think overall it'd be highly possible for Depp to do the role. Especially after what everyone has done with their roles thus far in the series, this seems to be a role he'd take. Depp usually takes on roles where he almost gets a lot out of them, can bend and twist and create as an actor and do what he feels is necessary for the character, much like Ledger with the Joker. Now if he were to do this with the Riddler, they'd have to be very careful to make him more dangerous, a lot more intelligent and more clever than Ledger's Joker.
After the chaos created in The Dark Knight, the Riddler would have to be absolutely 100% on top of his game, much like Jigsaw from the Saw series, planning everything out, making sure he'd know what would happen for every scenario. Almost have him O.C.D. or something. That could be something I could see Depp doing, while also showing off a side of him that is relatively insane, where maybe he talks to himself or sees things, give him a quirky sort of nature to show the weaknesses from his incredible knack of intelligence.
He'd have to go after Batman, obviously, making him out to be some sort of angel of death, completely responsible for the death of Harvey Dent, the upbringing of the Joker, Scarecrow and the likes of the other criminal personalities beginning to show their faces in Gotham, and try and twist and turn everyone's opinions around in Gotham. Turn everybody against everybody, make nobody trust anyone, have the entire city on edge. Or have him be incredibly techno-savvy, hacking into everything that makes Gotham run and holding the city hostage. He needs to have a hand that would be almost impossible for Batman to defeat to make him descent in the eyes of the citizens of Gotham again.
If they do go somewhat that route, if the Riddler is even the next villain at all, it needs to be something that will trump what the Joker let loose in Dark Knight. Hopefully they do pick Riddler. At this point, I think he's one of the only villains that can take it a notch up from the Joker and have it work realistically and I think Depp is one of the only actors I can think of that could handle the task and fit in brilliantly with the rest of the cast Nolan has already established.