Be discrete. You have nothing to gain from honesty in this situation.
Interesting. Same thing is happening with one of my colleagues. He let it be known that he is interviewing with other companies, so our HR department let him know that they are looking to replace him. He may be let go before he wants to go!
Discrete. If you are interviewing, but are not getting an offer, and they know about it, your employer will be able to take advantage of you (put more pressure, give extra work, etc.) and you will be stuck.