Zengue is Cameroonian, but played twice for Burkina Faso in the 2012 Nations Cup qualifiers against Namibia – matches Burkino Faso won, 4-0 and 4-1.
The Defender has a Burkinabe wife, and thus a passport from that country, but Namibia insist he does not fit any of the Fifa criteria to play for Burkino Faso, which include the stipulation that either a parent or grandparent must have been born in the relevant territory or that the player in question must have spent five years in his adopted nation.
The Confederation of African Football has twice rejected Namibia's case, most recently on November 24, but the southern Africans believe they should replace the Burkinabe at the 2012 Africa Cup of Nations.
CAF's reason for throwing the case out was mainly that the protest the Namibians lodged ahead of their second match against Burkino Faso, and Zengue, was not signed by either country's captain – a criterion which had to be met for the appeal to be successful (according to Article 37.1 of the 2012 Nations Cup regulations).
"It is a travesty of justice because CAF, for one reason or another, does not want to enter the debate of whether Zengue is eligible or not," NFA general secretary Barry Rukoro has told BBC Sport.
"That, to me, is just mind-blowing. We just don't understand why CAF does not want to enter that debate – and avoid doing so at all costs. For me, it flies right in the face of fair play and in the face of why we have regulations in the first place."
CAS will have to rush through the case, as Nations Cup squads have to be named on January 7, two weeks before the tournament's start.
Burkina Faso have been drawn in Group B with Sudan, Angola and Ivory Coast.