UPDATE: 6/10/10 10:30 PSTThe Wrap is now reporting that representatives of Joseph Gordon-Levitt have denied the rumor that the actor will appear in the film. We'll be sure to keep you posted if any new information comes forward.
Apparently, this sort of talk continued and the site now says that Levitt is being considered by Nolan for the part.
"Chris really dug Joseph [as an actor]," a source close to the director stated. "There was a joke at first between them [on the set of Inception] that Joseph wanted to read for Batman 3 and things heated up as filming continued."
This unnamed source then went on to say:
"It's not 100% confirmed that he's getting [the role of The Riddler] but there's certainly talk about it. Joseph is definitely on the short list."
David S. Goyer is presently hard at work writing the screenplay for the next installment in the Batman saga.