Adeyemi, 22, only joined the Blues last summer as a free agent, however Clark believes the ex-Norwich man has all the qualities of a leader.
"I have spoken to the board, (current captain) Paul Robinson and Tom about it," said Clark, speaking to the official club website.
"I just think he is future captain/manager/managerial material within his career. He is a very intelligent boy, he is our PFA (Professional Footballers' Association) club representative at such a young age and, usually, when he is fit he is going to play.
"He was taken aback when I spoke to him about it on Thursday morning, but delighted also. It's something you enjoy seeing when you tell a player some good news like that.
"So I've made the right choice and going forward in the future, he's a potential leader."