Carefully cut away any loose threads around the hole with sharp scissors.
Measure the size of the hole. Cut a piece of microfiber cloth a quarter-inch larger than the hole from an inconspicuous area of the couch, such as the back if the couch faces a wall.
Cut a piece of fusible web an inch larger than the microfiber patch. Fusible web can be purchased at fabric and craft stores.
Remove the paper backing from the fusible web. Center the microfiber patch on the sticky side of the fusible web.
Insert the patch and fusible web inside the hole on the sofa, with the fabric patch side up.
Place a clean cloth over the repair. Set the iron on a low setting for acrylic fabrics, and slowly press down on the cloth, running the iron smoothly back and forth over the repair to activate the glue on the fusible web. Lift the iron after several passes to check the repair. You might need to press a little harder or raise the heat slightly to achieve a tighter bond.