Can areola reduction scar be inside the areola instead of along the outside?

No, because it will not keep the areolae reduced and they will stretch again. Plus, that incision might impair the blood supply to your nipple.

Yes, you can design areola reductions within the pigmented part of the areola as opposed to the transitional area where the edge of the areola meets the breast skin. However, the closer the incision gets to the nipple, the higher the risk of sensory nerve injury (numbness) and damage to the nipple blood supply (necrosis).

If understanding your description correctly, the result would still be an incision around the outer portion of the areola. An incision within the areola may result in a more obvious scar due to pigmentation variance. I encourage you to visit with a board certified plastic surgeon to discuss your concerns and questions. Typically the incision results in a scar around the outer edge of the areola. Once mature this scar is generally acceptable and fairly inconspicuous.