Gourcuff, who had been in the post since summer 2014, told federation president Mohamed Raouraoua and the team on the plane flying back from an African Cup of Nations match against Ethiopia, several newspapers said.
The Algerian federation did not immediately confirm the news.
After three wins and a draw, Algeria are top of their qualifying group for the 2017 African Cup of Nations, needing just one win from their remaining games against Seychelles away on June 3 and Lesotho at home on September 2 to guarantee qualification.