What would cause noise (ground noise?) when touching the volume control and tone controls?

Back in the day, I had the same issue with an amp.  It had a two prong A/C plug, and turning the plug over, i.e., reversing the  prongs, solved the problem.

I guess since only one prong was supposed to be driven and the other was supposed to be a ground source, they must have wired the ground source to the chassis ground.  So if that prong was plugged into the driven side of the socket, the chassis wouldn't be properly grounded.  Turning the A/C plug over was the fix.

Your new unit probably came with a three prong plug that can't be turned over.  Maybe the internal wiring of the A/C connection needs to be switched.

If your preamp is a tube unit, it could be that you have a microphonic tube in the circuit, resulting in what you describe. If ss...not applicable.

@daveyf  I really should put more detail when I post. Yes, it is a tube preamp. I did tap on them gently to see if I could detect anything. 

@tubeguy76 Might want to experiment with swapping tubes around. See if that does away with the issue. I had this exact problem with my tube preamp, and with some tube swapping was able to zero in on the offending tube. Sometimes tapping on the tube will show an issue, but not always.

When I touch the metal top of the case in addition to the knobs, the noise will subside.

This sounds like the controls are not properly grounded and the case may not be either.

atmasphere +1

Probably the volume and tone control potentiometers bodies are not properly grounded.

If you have a multimeter, check continuity of the power cord ground pin to preamp case, also check volume and tone knobs to chassis continuity.