The Arsenal striker says his teammate only has one last aim to complete before he hangs up his boots, and says it will be "the perfect present" to claim the tournament.
The former Chelsea forward won the Champions League with his final kick of the ball for the west London club, before moving to China to join Shanghai Shenhua.
However, one trophy that still evades him is the AFCON, and Gervinho says that winning the tournament is the only thing left that Drogba wants to accomplish before retiring.
"[The Africa Cup of Nations is] the only thing left he wants to get for Cote d'Ivoire because he has brought us so much already," Gervinho told Goal.com. "That's the one last objective.
"I hope he will be successful. We will be with him. We will support him at the best of our abilities for him to be able to give this to the nation and then... maybe he will keep going but we could not ask for more from him."
The Arsenal striker also insisted that the former Chelsea man is a role model for a lot of young players in Africa, and part of footballing history on the continent.
"Yes, for me and a lot of young players in Africa, he is part of football history and of Cote d'Ivoire history," he added. "I'm very lucky being able to be next to the likes of Thierry Henry or Didier Drogba.
"I'm trying to enjoy it as much as I can. Before my first Cup of Nations in Ghana, I always wanted to play with him. I'm happy I'm able to do so... play with him, being close to him, laugh with him. Now I hope I'll win a trophy with him. It would be the best present ever for him, for me, and for Cote d'Ivoire."
Gervinho admits that the Cote d'Ivoire is in a tough group alongside Algeria, Togo and Tunisia, and says that he is aiming to reach the quarterfinals.
"It's a group where there are good teams and good players," he continued. "All the fans want to see good games. I personally don't see a team that we must absolutely avoid playing against.
"When you want to win a competition you have to play all the best teams. Whether it's Algeria, Tunisia or Togo. For me, the most important thing is to win my games and qualify for the next round. We need to start well against Togo and if we get the three points out of it we will have good confidence for the rest. None of the other teams are more important than another one. My aim is to qualify for the quarterfinals."