French-born Constant, who plays for Genoa in Serie A but has been the subject of recent transfer speculation, sent a fax to the federation explaining his reasons but they have not been made public.
Coach Michel Dussuyer did include Sochaux striker Abdoul Razzagui Camara who is still seeking to switch his international allegiance after being capped at under-21 level by France.
FIFA said on Thursday his application had only been received on January 3 and is pending the relevant investigation.
Guinea play in Group D at the Nations Cup with Botswana, Ghana and Mali.
The tournament runs from January 21 to February 14.
Goalkeepers: Aboubacar Camara (Alcoyano), Abdoul Aziz Keita (AS Kaloum), Naby Yattara (Arles-Avignon).
Defenders: Thierno Bah (Lausanne), Dianbodo Balde (Arles-Avignon), Ibrahima Sory Bangoura (Djoliba), Lanfia Camara (WS Woluwe), Morlaye Cisse (EGS Gafsa), Ibrahima Diallo (Waasland Beveren), Kamil Zayatte (Buyuksehir), Oumar Kalabane (Al Dhafra).
Midfielders: Mamadou Dioulde Bah (VfB Stuttgart), Habib Jean Balde (Universitatea Cluj), Sadio Diallo (Bastia), Pascal Feindouno (unattached), Naby Soumah (CS Sfaxien).
Forwards: Alhassane Bangoura (Rayo Vallecano), Ismael Bangoura (Al Nasr), Ousmane Barry (Etoile Sahel), Abdoul Razzagui Camara (Sochaux), Ibrahima Conte (Ghent), Ibrahim Traore (VfB Stuttgart), Ibrahima Yattara (Al Shabab).
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