The Lausanne-based sports tribunal said on its website on Thursday that it would be hearing the case.
Namibia have protested against Burkina Faso's use of Cameroon-born defender Herve Zengue (pictured) in two Africa Cup of Nations qualifiers against them, saying he was not born there, had no blood ties with the country and had never lived there.
They went to CAS after the Confederation of African Football (CAF) threw out their protest on a technicality.
Football's governing body FIFA has said it cannot get involved.
Burkina, drawn in Group B along with Ivory Coast, Sudan and Angola, said Zengue was given a passport because he was married to a Burkinabe woman.
FIFA statutes say however that, in addition to being granted nationality, a naturalised player must have lived in his adopted country for at least five years.
Zengue, who plays for top-flight Russian club Terek Grozny, has not been included in Burkina's Cup of Nations finals squad.
Namibia lost 4-0 away and 4-1 at home to Burkina but want to be handed 3-0 forfeit wins for each game.
If they are successful they will top the group in Burkina's place.
"We know we have got a case and it would not be good for us to go to the Nations Cup without prior preparations," Namibia FA President John Muinjo told the BBC while announcing his squad would begin training immediately.
"It's our ultimate goal to play at the Nations Cup, everyone is positive. We have to take a team that is adequately prepared."
The Cup of Nations, being staged in Gabon and Equatorial Guinea, kicks off on January 21.
