French football federation president Noel le Graet has been told to quit by the head of the organisation's ethics committee over his comments about Zinedine Zidane.
Le Graet was criticised for saying he would not take a call from Zidane about the role of national team manager.
He later apologised for the comments, which he described as "clumsy".
However, the FFF's ethics committee head Patrick Anton says it is time for Le Graet, 81, to step aside.
Anton told L'Equipe: "Le Graet has made comments that show he has lost some of his lucidity. He is a man who is tired, who needs to move on."
Zidane lifted the 1998 World Cup as a player and enjoyed a trophy-laden spell as coach of Real Madrid.
He had been tipped to succeed Deschamps as France manager after the team's defeat to Argentina on penalties in the World Cup final, but on Saturday Deschamps extended his contract until 2026.
Le Graet's comments about Zidane were branded "disrespectful" by France striker Kylian Mbappe and goalkeeper Hugo Lloris, while Real Madrid also criticised him.