Making the first move without looking desperate...

Just tell him, chances are that he feels the same way if you're getting this vibe, I would know because I sound just like the guy you're talking about, otherwise chances are that nothing will happen between the two of you.

You're in a rather good situation!. Make the small moves as suggested by sammy123. Don't try too hard, just build up the pressure very slowly by doing these little things. Everything else will fall in place naturally, after sometime, and he would probably ask you out or something.

well he likes you for quite some time. If you have developed a liking for him you can show it to him also. like being near him. sometimes find some stupid reasons to talk to him. or if he tries to approach you, don't run away. This last one is the most positive response you can give.

if you think he likes you, its a start, that means he likes you being you. I think you shouldn't over do it and just be how you have been. it will eventually come up, I'm sure

Just joke around that you'd be the cutest couple ever. Be like "we're getting a minivan right? definitely with a white picket fence though because everybody likes their privacy, 2.5 kids. and a six figure income." just be like that and he'll get the idea.

and if he doesn't, then maybe he doesn't like you after all because seriously, nothing has ever stopped a man from getting his woman.

Well you could just keep it real casual. Like "Hey, we should go out sometime." The problem with this is that they might not know that you mean on a date. So you could just do what I've always done in this situation. Just kiss him. Find a moment alone and pull him close and kiss him. Then say something like "I've wanted to do that for a while." Guys seem to really love this, and for me it was a lot better than asking awkward questions.