Years ago, I worked at a zoo. One day, as I stood in the East Asian Forest exhibit, a visitor walked up to me.
'Hey, how much do I have to pay to pet the leopards?' he asked. I stared, waiting for him to say he was kidding.
'Um, we don't let visitors do that,' I finally said.
'That's not fair,' he said. 'You guys get to play with them all the time.'
'We don't,' I said. 'They're wild animals. And they don't want to play with us. Unless it's the way cats usually play with their food.'
Mr. Leopard Snuggler, I think, was probably influenced by the myriad media representations of non-domestic animals being cute little cuddlebugs for the right human. As far too many unfortunate humans demonstrate, this is not the case. No wild animal can become truly domestic, even if raised lovingly by humans since it was young. Even domestic animals can act unpredictably or aggressively without appropriate socialisation.
If you want to give your character a cool pet, there are plenty of interesting and useful domestic animals. An animal which wasn't fully socialised can even provide a 'character tames skittish animal' subplot if you wish. Or if you're writing speculative fiction, there are a lot of options for a magically or scientifically enhanced critter. But please, no leopard snuggling. Being a zookeeper is hard enough work without having to keep people from trying to pet large predators.