Absolutely...just glance over to him...have a smiling expression on your face...lock eyes for a bit so that he knows without a doubt that you're not just looking in his direction, but at him, then when he smiles back or after a couple seconds, whichever happens last (you don't wanna stare!) casually look away back to what the professor is saying or whatever. Don't do it often..just a handful of times during the class session, if that.
Point is to make it so that he knows you are interested and open...so that he's comfortable to make a move and approach you. (then again, I'm one of those I want a guy to approach me types...if you are not then I guess once you feel comfortable with his level of interest, then from there do what ya do!)
I'd just continue smiling. When you catch him next time I'd look at him, blush and look away. Just a bit mysterious, leaving him wanting something more, hopefully something that will make him take the initiative and come to you out of class. Go ahead and wink too if you're comfortable, not going to hurt you any! Good luck =)
I would smile so that he knows your interested and if he still doesn't approach you he could just be shy so try saying hi-dont make the same mistake I did by just staring back because he might just go and get a girlfriend and then it'll be too late to do anything about it. Good luck :)
Based on the information you gave it's impossible to tell what might be going through his head, but if YOU like him a smile from across the room can't hurt. Just be casual about though, not too intense or too frequent and see how he responds. Plan your next step after that.