After switching his allegiance to Côte d’Ivoire, Zaha has been included in their provisional squad for the 2017 Afcon in Gabon.
He was born in Abidjan but moved to south London with his family when he was four years old.
Allardyce who was just appointed as coach of Palace after the sacking of Alan Pardew wants to forward to remain with the club as relegation battle thickens.
If he chooses to play in the Afcon, Zaha will be away from Crystal Palace for close to five weeks and Allardyce thinks it will be a blow to the club who are 17th in the Premier League table just two points off the relegation zone.
Côte d’Ivoire kick off their 2017 Afcon campaign with their first Group C game against Togo on Monday, January 16.
If Côte d’Ivoire get to the final, Zaha is expected to miss crucial league games against West Ham, Everton, Bournemouth and Sunderland.