Preamp Turned Down/Amplifer Noise

When I turn down my preamp all the way (doesnt have a mute) I can hear what sounds like a hum through my amplifier. This could be transformer hum I am not sure. With the preamp volume all the way down should there be dead silence through the speaker. Is this a ground loop issue?
Sounds like it, but you do not provide enough information. Is this a new development or has the hum always been there in this system? Is there a television, cable or satellite connected to this system? Did this condition start after adding a new component? Is your power from dedicated lines or are you in an area of known "dirty" ac from the wall? Have you added any household appliances or flourescent lighting recently?

You can start by lifting the ground off your components with a cheater plug. If the hum goes away, you should be able to isolate which component is causing it, then you will be faced with a decision of trying an alternate grounding method, lifting the ground from that component, or replacing that component. If the problem is from video, there are ground isolation devices for video that are relatively inexpensive. Also check your cable management and keep power cables away from IC's, speaker cables, and video cables. Search some more here and at Audio Asylum since there has been much posted on this subject. Good luck.
I have had the this noise when i was using speakers with a high sensitivity rating like 90 db and above. They seem to show more electronic noise.
If your pre-amp has an adjustable gain like a surround pre-amp or a receiver try setting it to a lower gain.

Good luck !!
You are getting the hum from the amplifier or the speakers? If you are getting it from the amplifier, it may be a fan or a transformer hum (I am assuming you need to get pretty close to the amp to hear it).

FWIW, I had a 3-way light in my listening room and somehow the wrong type of lightbuld was put into it. Whenever the light was turned to dim or moderate, I got a hum out of my amp. At full bright or off, I got no hum. I unplugged the light until I got a new "correct" light bulb and all is good now. If you have a dimmer switch nearby, check this as well. If all the way off, does the hum go away? Same with other demanding appliances as referenced by Mitch2.

Typically a ground loop hum is going to be exhibited through the speakers and quite noticeable. What happens if the preamp isn't turned on? Does the home disappear?