Just to clarify - engaged is clutch lever out, disengaged is clutch lever in. If you "let the clutch out", you're egaging the clutch.
If you hear noise in neutral when your clutch is engaged (lever out), then it may be your throwout bearing. Was the clutch replaced recently? If it was, it's probably not an issue - a lot of places will use too little grease on the throwout and it will keep spinning even when the clutch isn't engaged.
Try just squeezing your clutch, not enough to actually disenagge fully, and see if the rattling goes away. If so, probably bearings. If you haven't had the clutch replaced recently, you might want to look into it.
If the clutch is out and you're hearing tranny noise, that's a whole different matter...