Clean it with bleach and a scrubber
Why are you faucets green in the first place. Do you not clean them weekly? Use Clorox disinfecting wipes at LEAST weekly.
It could be limescale. Try spraying a mixture of vinegar and Dawn dish soap on it (50/50). Let it sit and do the work, then scrub with an old toothbrush.
Try bleach on an old (soft) toothbrush.
I put vinegar in a sandwich bag and put it over the end of the faucet....holding it with a rubber band. I leave it overnight and the screen is clean in the morning. I think if the green stuff is around where your faucet comes out of the sink, you can put a rag soaked with vinegar around it and leave for awhile...may have to moisten it with vinegar again.