Should I Ask My Supervisor to Hang Out Outside of Work?

I’ve been at my new job since February and I have this supervisor who is really cool and we have a lot of similar interests. It’s always me starting the conversations first though but I feel like it’s mainly because he’s always focused on working and I’m always focused on slacking off but he does listen to my antics and laugh. I just feel like he has yet to actually show his full personality due to him having to be in charge and always work focused. With that being said, should I ask him if would like to hangout outside of work. He’s an introvert like me, so I don’t know what’ll he say but he’s very nice and interesting.