Nick Wilde was an observant creature, and he most definitely noticed the 'looks' Gideon Gray gave Judy Hopps, his coworker, partner and best friend. And he didn't like it one bit. Not that he was jealous. I mean, sure, he was upset that he got fewer cases with Judy, it was hard to find a good partner at the ZPD) but it wasn't that he liked her or anything ridiculous. He was just looking out for her. That was all. Nothing else. She was her partner-in-crime, his coworker and best friend. So what if she was adorable when she was happy, upset, angry, and generally at all times? So what if she challenged and pushed him to be a better animal without even trying?
Their relationship was purely platonic. Judy had no romantic feelings for him, so he wouldn't have any for her.
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Judy Hopps didn't particularly like the newest cop, a zebra named Chantelle. She was glad that Chantelle wanted to be around or with Nick so much, but it was irritating. She never got any cases with him anymore. Judy wasn't jealous. Not at all. Because she didn't have a crush on Nick. He was her partner-in-crime, her coworker and best friend. Their relationship was 1000% platonic. But that didn't mean she had to like Chantelle. So what if his stupid smug smirk was the cutest thing? So what if he helped her out of countless sticky situations? So what if he probably was the best thing to ever happen to her?
Whatever was between them was purely platonic. Nick had no romantic feelings for her, so she wouldn't have any for him.