This is a tough one. Only confront the individual if you heard him/her say it first-hand. If it's something somebody else passed to you, be very, very careful. In my experience, employees like this are trying to uncover weaknesses in your management style. S/he is saying what they are to try to get to you...don't fall into the trap.
I'd find a way to turn it into a positive, without a confrontation. In the next departmental meeting, I'd put a spin on the rumors, without actually mentioning them. You don't want to appear as if you are buying into the rumor mill. I'd probably talk about all the opportunity there is in the department or the company. One of the lines I always use is "the best way for me to get promoted is to prepare one of you for my position". That usually gets two points across: first, that I'm interested in the career development of my employees, and second, that I'm not in fear of losing my job to one of them. You have to mean it of course....meet with your employees one-on-one at least once a quarter and check their progress. You'll be surprised at how well they'll react that you're taking an interest in helping them to move forward. In my experience, the folks that work with you will advance and those that don't will eventually become so unhappy at their lack of progress that they'll move on. Lastly, document, document, document. Take note of every insubordinate action. Eventually, people's attitudes come out in their work. If you have enough evidence, you can take care of the problem that way.
Good luck to you!