Privately ask the individual if they are indeed looking for another job. Most people will answer honestly.
Find Out Why
You may find out that the person is not unhappy with the job, but rather has a personal crisis that is affecting his or her work. If there are other reasons, and you truly value this individual, you may be able to reach an agreement that keeps the person with you. At the very least, you'll learn of situations that could be making others unhappy.
Don't Make a Counteroffer
If the employee has already accepted another position, it's probably best to let them leave. Counteroffers are seldom successful in ensuring long-term continuity. Research from Robert Half International shows employees who accept counteroffers are no longer with the company as little as a year later. The reasons that prompted them to move on are often too strong.
Wish Them Well
If an employee has accepted another position, wish him or her well in their pursuits and leave the door open should they decide to return.
SOURCE: Robert Half Reports, Robert Half International Inc., Los Angeles, CA. Volume II, 1996.