The Lille shot-stopper is optimistic about the African champions' chances at this summer's tournament in Brazil
The reigning African champions have never made it past the round of 16 on the four previous occasions that they qualified for the final, but the Lille goalkeeper has little doubt they can cause a surprise this time around.
"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 will possibly meet France in the first round of the knockout stages, but the Lille goalkeeper is not thinking about taking on the country where he's been plying his trade since 2011.
"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.
"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."
Nigeria meet Argentina, Bosnia & Herzegovina and Iran in the group stages.