"I think we are going to make big progress," Enyeama told the official Fifa website.
"We are focused on the World Cup, to make Africa the proudest continent.
"Ghana almost reached the semi-finals four years ago. We are going to achieve a better result and be the first African team to get to the semi-finals of the World Cup."
Nigeria are likely to face France in the first round of the knockout stages, but Enyeama, who is currently first choice for Lille in Ligue 1, is not fazed about that.
"If we play against France, it will be interesting, but if we play against Switzerland, it will also be interesting. The important thing is to qualify," he said.
"Playing France for a place in the last eight is not really what matters to me right now, I just want the team to make it to the second round.
"But maybe we will come out first, and then we will not have to play against France."