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Vulture caught up with the director this week and asked him just that, and Cuaron said he would be interested to jump back into the magical world.
"'Azkaban' was fun to make, and when I did it, I was invited to do the next one, but I didn't want to overstay the welcome, because it was such an experience," Cuaron told the site. "But now? Why not? I do have stuff that I want to do [next], but a J.K. thing ... "
Of course, as the director noted, there's no offer on the table from filmmakers -- "They haven't called me yet!" he said -- and no guarantee that one will materialize. But putting the word out can't hurt.
"Fantastic Beasts and Where to Find Them" will be based on a fictional textbook used by Harry and his friends at Hogwarts, and feature the adventures of its author, Newt Scamander. No word yet on a timeline for the movie or potential casting, though we know one director who might be interested.