Snare Wire Noise
How can I get my snares to stop rattling when I'm not playing?
Different muffling techniques can help with this problem. Be careful not to dampen the drum too much as it will create a dead sounding snare. Another thing to try is simply tuning your drum higher or lower. The four tension rods on the snare side closest to the snares can make a big difference when detuned. The room you are playing in will also have a lot to do with this noise. After all, you are getting this issue due to sound reflection. Try positioning the kit in a different area of the room.