You can make your own gift wrap from some of that fabric in your stash. Encourage the recipient to re-use the bag to give other gifts or for holding stuff. My nephew holds his rock collection in a bag I gave to him. If everyone did this we would reduce the paper waste in our environment. The Japanese have long used gift cloth, called Furoshiki, for presenting gifts. In the Japanese tradition, the giver keeps the fabric.

You can make a bag in a few minutes. You can also Embellish the bags or use Photo Transfers to make personalized bags.