|It sounds like your employee needs to focus more on getting his job done, and less on getting your job. While it is appropriate and important for employees to have some clear career objectives, there is more to a career objective than repeating it to anyone within earshot.|
If this individual's objective is to advance in the company, whether into your position or any other slot, his performance will need to be more than "generally satisfactory." And, that is the key point to express to him. He needs to understand that his current objectives should be focused specifically on his performance and productivity if he truly desires to be promoted.
So, rather than telling him that you are extremely tired of hearing him express his dream to obtain your position, try to focus your comments on the specific kinds of steps that he will need to take in order to have a chance at advancing into any position. If he continues to direct his effort on job dreams rather than realities, he needs to understand that the dreams will not be coming true.
There is a real strategic advantage in having an employee who can advance into your position, since this obviously makes you more promotable. However, the individual who ultimately moves up in your department must distinguish himself or herself by work that is widely acclaimed, rather than by merely making a claim.