Disconnect the roll from the desk, which may be the hardest part of this job. Find the screws that hold the roll into the groove of the desk. Look at the top of the roll through the back of the desk or take out the top drawer and look at the underside of the desktop to locate the screws.
Lay the roll flat, face down, on a surface large enough to accommodate it. Prevent scratches to your work surface by putting down some newspaper or other protection first.
Remove any of the old fabric and glue. Use a 2-to-1 ratio of warm water and vinegar to help loosen the old glue if necessary.
Measure the length and width of the roll. Use a heavy-duty piece of fabric such as canvas. Cut the fabric to those measurements.
Buy glue that is specifically for attaching canvas to wood for projects such as this. Keep in mind other glues, such as plain wood glue, get brittle over time and will not hold up to a lot of use.
Pour some of the glue into a Styrofoam bowl. Lay the fabric face down on your work surface.
Apply the adhesive to the backside of the slats using the paintbrush. Use enough glue to hold the two together, but don't use so much that the glue seeps out through the front of the slats. Do not put glue all the way to the end of the slat. Leave ¼ to ½ inch free of glue.
Leave about a credit card's width between each slat to allow for fluid movement when you put the repaired roll back on the desk. Press the slats into the fabric using your hands to help it adhere.
Weigh down the slats with a heavy object such as a book to hold everything in place until the glue dries. Let the glue dry overnight.
Reattach the roll to the desk.