The sides meet in Brussels in what will be the first of a series of friendlies building up to the competition in Brazil this summer.
The likes of Kompany, Eden Hazard and Romelu Lukaku are among Belgium's brightest stars, while Ivory Coast can call on Yaya Toure, Didier Drogba and Gervinho.
Manchester City captain Kompany believes both countries could cause an upset against the bigger names in Brazil.
"The World Cup favorites are the usual suspects - Germany, Spain, Argentina and Brazil. Behind them I see a group of countries, which sometimes cause a surprise," he told Het Laatste Nieuws. "I reckon [these] include Colombia, Chile and Japan as well as Belgium. Ivory Coast also has a very strong team. They may also be a surprise at the World Cup like a lot of other countries.
"There are teams that have more talent than Belgium. Based solely on our talent, I do not think that we will win the World Cup. That can only be done with some luck, if everyone plays very strongly and if we have a strong team spirit."
Marc Wilmots' side will be fancied to progress from Group H ahead of fixtures with Algeria, Russia and South Korea.