I sent someone this in a message, but I suppose it is relevant here.
My opinion is that the boss will be male. Gosho follows a simple rule 3 times out of 4: a woman will have a man in her circle of people who interact with her who is on average more competent. Competence is measured as the ability to solve cases, make plans, outsmart opposition, or command a dangerous situation.
Proves the rule
Ran <-- Shinichi
Ai/Shiho <-- Conan
Ayumi <-- Conan
Sonoko <-- Kaitou Kid, Makoto, Shinichi
Yukiko <-- Yuusaku
Kazuha <-- Heiji
Sumiko <-- Shiratori
Azusa <-- Amuro, Kogoro/Conan
Masumi <-- Shuukichi, Shuuichi, Shinichi
Yui <-- Kansuke, Koumei
Jodie <-- Shuuichi
Kir <-- Shuuichi, Ethan, Shinichi
Chianti <-- Gin
Aoko <-- Kaito
Chikage <-- Toichi
Akako <-- Kaito
About even or in violation (and note that for all of these but Naeko, the woman has been in trouble more times than the man has and needed rescuing.)
Eri <-- Kogoro
Sato <-- Takagi
Naeko <-- Chiba
Vermouth <-- Gin, Akai, Bourbon
Character pairs we don't know enough about: Shizuka and Heizo, Mary and Mr. Akai/Shuuichi
Vermouth is likely less competent than the boss, so to prove the rule that boss would be male. If the boss is top in competency then only a male boss would avoid violating the rule.