I think it could be either of Ai's parents more likely the mother as this would explain why Vermouth is so trusted they could be best friends.
I don't think it's Agasa because of Ai, if he was the boss he would either hand her over himself or get Vermouth to do it, why tell Conan. If he wanted to keep an eye on her I don't think he would have people searching for her when he could easily be killed if found since most members don't know his identity.