Somalia wants to keep power over the largest amount of land that it can, so it will for the predictable future say "no".
Countries can accept a self-determination process in a breakaway region, recent examples include Timor-Leste and South Sudan. In the latter case, the independence process was agreed under pressure from donor countries but not in defiance of Sudan's government. Besides avoiding sanctions and other diplomatic benefits, it can be a way to end a costly civil war. Obviously many countries also refuse to entertain similar solutions but it's not the case that every government anywhere will always categorically block any territorial change.
I think the AU should instead preside over talks between the Somaliland and Somalia to decide the future diplomatic status of Somaliland.
Obviously talks cannot happen without the consent of Somalia. I am pretty sure the African Union would be ready to broker such talks if there was any interest on Somalia's side but it has to defer to it if it hopes to achieve some sort of negotiated solution.
Incidentally, it's not unusual to need lengthy negotiations on the terms and logistics of negotiations before the parties even agree to publicly declare they are ready to talk to each other. The first step would probably be to name a special envoy to explore the feasibility of such talks.
If talks are not possible, one might wonder why the African Union doesn't take a stronger approach, perhaps organising or somehow supporting a referendum, officially condemning Somalia or pushing its members to unilaterally recognise Somaliland. And the reason not to do that is quite clear: At the end of the day, the African Union is little more than the sum of its members and many of them have breakaway regions, rebellions, separatist movements, or minorities and have no reason to create a precedent for some international organisation or foreign country forcing the independence of a territory without the consent of the central government.