Leon is an animal lover, he'd never admit that secretly inside his heart warms when he sees a cute dog or cat, sometimes he'll even see a deer and it brings him a sense of peace and joy.
In his line of work, he doesn't have time for a pet of his own, so he does interact with any cat or dog he sees as low key as possible, he'd hate to be caught cooing at some cat for purring.
However, if you have an animal or if he ever got one, here's how it'd go down;
He prefers cats over dogs, he does like dogs but he relates to cats more in the sense of being more mysterious and introverted.
If he had a pet, it's obviously be a cat, something flurry that'd sit on his knee whilst he was watching TV or whatever, he'd mindlessly stroke it to calm himself down, relaxing as the little thing purrs.
He'd take it to bed, smiling as it lies on his chest and sniffs his face, helping to ground him when the bad memories come at night.
His cat is very important to him. When he brings you to his place for the first time he'd introduce you to the cat as if it was a person, he's kind of nervous if you both don't get along, however you and the cat become BFFs. Seeing you with the cat melts his heart and kind of turns him on, he's happy his companion approves.
If you had a cat, he'd definitely try to play it cool, but soon become too attached and will insist on giving the cat a nickname and having it sit on his lap. He adores your cat, treating it like his own, he kind of sees it as the child in your relationship, both of you bond and care for the cat.
Also, imagine him playing with the cat, sitting cross legged on the floor with some stringy toy, chuckling as the cat rolls over and kicks its legs. You'd come in to find Leon grinning up at you, his blue eyes brighter then ever as a small blush covers his cheeks from being caught out.