The Elephants topped Group D after drawing their final game with Algeria and face a tough test against the dangerous Eagles at the Royal Bakofeng Stadium.
Drogba, however, is confident his team – who are tournament favourites – have the quality to come out on top.
“Against Nigeria, it will be a tough game, against a team that also intends to go far in this tournament,” Drogba said.
“The Super Eagles are a very strong team, very physical.
“Stephen Keshi has been doing good work, but I hope that Côte d’Ivoire will win and go through, but it will not be easy.”
The former Chelsea striker is looking forward to playing against old club team-mate John Obi Mikel, who will anchor the Nigerian midfield.
“It is going to be hard and tough, everybody knows how good Mikel is, and what he did with Chelsea in the Champions League final,” Drogba said.
“He was one of our best players in that game. But now I will play against him.
“We are going to laugh before the game, and then it will be tough during the match, but then laugh again after the game because we are good friends – he is my brother.”
Mikel, for his part, is relishing the burden of being the Eagles’ talisman and is confident his side can cause an upset against the fancied Ivorians.
“The pressure is even more and I’m primed to carry the burden and try to lead this team to a very successful tournament,” he said.
“All of us are doing everything we can and the players are all in good shape. The team is together and all we have to do is just keep doing what we’re doing.
“The quarter-final is going to be an opportunity for us to go out there and show the world what we can do against the Ivory Coast.”
Nigeria enter the quarter-final with momentum after defeating Ethiopia in their final Group C game, thanks to a double from Chelsea winger Victor Moses.
However with the Elephants boasting players like the Touré brothers – at Manchester City – Arsenal’s Gervinho, Salomon Kalou and Wigan Athletic’s Arouna Kone, the Nigerians will need to raise their game to avoid a tournament exit.
The winner of the game will face either Mali or tournament hosts South Africa in the semi-final on Wednesday in Durban.