I’d recommend darning. Get a white thread and zig zag across the hole using really small stitches with low tension, and that should be nearly invisible. See link for a really cruddy diagram! cruddy diagram

The difference between this and just sewing it up is that the stitches lay flat, rather than having a raised bump like you would with a whip stitch, and the edges are covered to prevent fraying. By weaving over and under, including at both ends, the tension from the stitches is distributed over a larger space, so it doesn’t just tear where you put the stitches in later.