In my experience, a noise in neutral which stops when you depress the clutch is coming from the gearbox itself.
When you depress the clutch, the innards of the box stop moving and the noise stops.
Some vehicles tend to make this noise when the oil gets hot but when the oil is cold and thick they are quiet.
It could be that you need to add oil or use a thicker grade.
Of course it could also mean that you have a bad bearing or some other worn component but I've got my fingers crossed that its not that.
I have also had a throwout bearing that seemed to do that too though they usually make noise only when the pedal is depressed and under load.

cheers,  Steve