Is it a sort of resonance coming from within the body? It could just be the springs etc. in your vibrato resonating. I occasionally get something similar.
Can you hear it through your amp? If not then don't worry about it. If you can, try packing the vibrato cavity with tissue or something to stop the resonance.
Also check your
locking nut is tightened, check the tuners, vibrato arm and all other components on your guitar. It could be something as simple as a loose screw.
Hope this helps you. Good luck!