Are you certain that he is a free agent and a nice person and not just a flirt?
If so, you could just ask him outright ~ difficult, I know ~ and he might be too shocked to give you the answer you want, anyway.
You could ask him by text or e-mail or letter.
If he really likes you, and knows that it is your last day, he might say something to you, anyway.
What do you think he would say, if you just pointed out to him that it's your last day, so he won't be seeing you any more ~ no more office chats, etc. You could say that you will miss him, because you enjoy his company ~ and give him the chance to respond accordingly.
