When your trem is at rest, are the spring coils all stacked? Meaning, are the springs completely or nearly at rest? I've found that if the springs are completely at rest, as you pull up on the trem arm the coils can rub against each other and if there's even a little bit of rubbing between the coils, they'll make a bit of noise. The coils should be smooth, clean and without any roughness between them.
Some of the others already asked if the trem was loose or sloppy feeling. Could mean that you need some new springs or a set up.
How many springs are you using and what gauge strings are on your guitar? A picture of the spring pocket would be nice. Are we talking about a full floater or a blocked trem?