On their 22nd appearance at the continental gathering, Ghana failed to progress past the Round of 16, for the first time since 2006.
“If he [Akonnor] becomes the Black Stars coach he will be great," Addo was reported to have said in The Finder.
"He is my friend and I will always push for it. For now, we have to wait until a decision is taken on Appiah or if he decides not to continue anymore.
"Having said that I think C.K has done very well on the local scene. He has played for the national team and captained a foreign team as well.
"He has all the experience but we have a coach now so anything I say will not be appropriate but if there is a change then yes Akonnor will be perfect.”
Akonnor's future at Kotoko remains bleak following his re-assignment from head coach to technical director.
Reports say the former Ghana international is unhappy by the decision of the Porcupines' management and could be headed for the exit.
The former Dreams FC and Ashanti Gold boss led Kotoko to win the Ghana Special Competition in June after guiding the team to the group stage of the Caf Confederation Cup last season.