It's likely the mainshaft bearing in the trans. Possibly a pilot bearing, but if it is a serious, deeper sounding grinding, it likely is inside the trans.
What's happening is the mainshaft of the trans always spins with the clutch is not engaged, even when the trans is in neutral. Thus you hear the noise. Depress the clutch and the mainshaft is no longer spinning - noise goes away.
Should also make the noise when the car is moving, though it can be hard to hear.
Throwout bearings make the most noise when the clutch is pressed. If they are bad, that's when you'll know it.