Pixar's Monsters Inc. (2001) is not only a great piece of storytelling, but also sports an unrealized link to Godzilla.
At about nine minutes into the film, Sulley (John Goodman) and Mike (Billy Crystal) greet a large, green, bipedal monster named "Ted" while walking to work. The audio commentary reveals that Ted was meant to respond to Sulley's salutation with the recognizable roar of Godzilla himself. But (surprise, surprise) they were not able to secure permission from Toho, so Ted ends up clucking like a chicken instead (a choice the Pixar guys admit was "bizarre").
Kaiju fans will also be interested in the Blu-ray disc special feature that takes viewers behind the scenes at Tokyo Disneyland, where a Monsters Inc. ride continues the story. Evidently, many Japanese fans dress up as their favorite Disney character to come to the park, both children and adults alike. And, yes, Ted makes an appearance too. In the movie, you only see him from the shins down, but on the Monsters Inc. ride, he is fully visible. While he bears a strong resemblance to Pete's Dragon (another Disney character), the homage to Godzilla is fairly obvious--and where better for him to dwell than Japan's own Disneyland?