In most cases, it is ok to store an expandable garden hose on a reel. However, these hoses often shrink to a moderate size that you can coil without a reel. If you choose to use a garden hose reel, the best approach is to ensure that your hose is entirely empty of water. After you've drained all water in the hose, there is no reason you can't wrap it onto a hose reel for storage.