The 28-year-old is on a self-imposed exile from international football following a dispute with the Togolese federation over match bonuses.
However, Six is hoping to persuade Adebayor to settle his differences and join up with the Togo squad for the tournament, which kicks off on 19 January in South Africa.
"It's clear that we will need Adebayor but don't forget we qualified without him during one of the play-off matches," he told Le Buteur.
"I am doing everything I can to get him to come back to us. He's a world-class player and the Togo national team captain. He is very important to the group.
"I will put all my strength to get him to change his mind but he has the last word. This is about more than just him sending a warning to ensure Togolese football moves forward."