This is a hard situation because he is engaged to someone else so it really isn't a good idea to start anything with him until he decides what he wants and whether that means to break off his engagement or if he is just being friendly with you. Seeing that the two of you work together and your boss has already questioned your relationship you may be playing with fire or even get fired if he thinks the two of your are dating outside of work. I would not say much especially at work because that could be cause for him to file a complaint or get you in trouble with your boss so make sure that he is feeling the same way about you that you are about him but even still his fiance has to come to mind and how she would feel to know that someone from his job was talking to him about feelings they may or may not have for each other. Just be careful what you say until he makes the first move and if he does not then wait until outside of work to talk him about this. You do not want to jeopardize you job in anyway.
Just come out and ask him and tell him it won't affect the friendship you have at all, it's time to get those pent up feelings out in the open so that you can both move past this tension and decide what the tension means. Sit him down or maybe ask him to go to lunch in a public place and talk to him about everything his actions and yours. There is no other way of going about it where you can get your answers and keep the meeting noble and mature so not to hurt anyone's (fiance') feelings.