Originally Posted by Atra Militis
There is small spring attached to the clutch actuator or whatever the technical term for it is, but you just have to throw some grease on it and the squeek will go away. It's sitting behind your TMIC. You description of the noise sound very similar to the one I've experienced and mine has been fixed once I figured out what it was. Still on original clutch running 46K strong! Hopefully this input may have helped.
Here's a video of what my car's clutch sounds like when it's being pressed in.