That's why I don't date co-workers. If things become awkward, you almost have to deal with that person everyday. If the relationship does go well, do you keep it a secret or open it up to co-workers and possibly HR might have to be involved. I rather be good friends with that person. When the day when you or the other person doesn't work there anymore. Then pull the trigger to ask that person out, if they are still single.
One job I had, there was a co-worker I kinda had a crush on and we both knew we were gay. He did ask me once if you might want to get a drink. Unfortunately I did turn him down, because I didn't want to date at the work place. Like a month later for the fun of it. I did ask him the same thing and he turn me down and I found out he was dating someone. I probably regret never going out with him now, who knows how our relationship would have gone?
There was another situation, were this one girl and I became great friends. We both really likes each other and people thought we were going out, which we didn't. But we did act like a married couple at the job. Years later when she was let go and I was working for another company. I invited her to be my date at the company party. Which I glad because we our relationship turned serious for couple of years. Unfortunately the relationship ended do to some family issues.