There aren't really any explicit quotations, but that fact that his name is 'Goole' which sounds uncannily like Ghoul is a huge indicator of the supernatural. Also, note the way he can encourage confessions that work to his advantage and the way he appears to be omniscient and only present at the house to receive confessions. It's as if he already knows the answers to his questions but what you need to remember is that this play was written in 1945 and based in 1912 so Priestley wrote the play with 33 years worth of hindsight and was therefore able to predict future events. Obviously, he wasn't an Inspector and we are never told who or what he was so all we can do is wonder...