Probably your clutch release bearing. This bearing is normally not under any pressure when not in use, which is why it can be noisey, but when you press the clutch pedal it applies pressure to the clutch release springs on your clutch pressure plate. The pressure will stop the noise from occuiring (in most cases.)
The solution is to replace the bearing - a pretty major job absolutely NOT worth doing until a worn out clutch is to be replaced.
Many many vehicles have this problem but they will run almost forever like this without any harm being done.
Mine only does it when it's cold.
Hope this helps,
Ron.