Feelings towards a tutor...

I am a 19 year old in college. Recently, a new tutor started work there. He covered for a few of my classes and we got on really well. We spoke a lot, he was very kind, funny and attractive and we got along extremely well. Now I have my normal tutor back, but I can't get him out of my mind. We see each other around and smile but never don't have any real contact. I really want to get to know him better, but I A) never get a chance to speak to him and B) think it might be inappropriate with me being a student. Would it be inappropriate for us to know each other better? And how do I go about getting a chance to talk to him?