How to stop ratte from gnawing on drywall?

So I have a pet ratte named Jerry who decided he doesn't like the wooding chewing logs from PetSmart. This is fine, but we don't have a ball for him to run around in yet outside of the cage! Whenever I let him run around my room, he tries to gnaw my wall, and is scraping the sheet rock off with his teeth! I can stop him while he is doing it but his attempts are relentless. He needs time outside the cage, but this is bad for him and bad for the house. How to get him to stop?

P.S. He also has a tunnel made of soft plastic (the kind that crinkles) and fabric. He shreds the fabric on that with his teeth. Does this have to do with anything?