I think if you put anything down, he'd just try and dig through it until he successfully arrived at the bottom... where you'll find him digging away at the plastic.
They way I've dealt with my little one digging on her plastic is to decide it's cute rather than annoying since I can't really change her behavior in that regard. I also have a blanket between her cage bottom and the desk it's on. Seems to dampen the noise a bit.