If it goes up with the volume control, then it must be coming in before the volume control. Ground current noise adds to the signal and does not change with the volume setting, so it must be on the input signal line. It could of course be the source, or (more likely I would guess) it's picked up by the circuitry or interconnects.
To check, first use shorting plugs on the input and see if that kills it. Try at all volume settings; if it is gone at zero and at full volume but loudest around 80% of the volume control then it is picked up at the volume control output.
If it is gone with shorting plugs, try again with nothing plugged into the inputs. If it is quiet at zero volume and maximum at max volume, then it it picked up by the wiring between the input jacks and the volume control.