The two Frenchman share a close relationship at the Bernabeu, with Zidane credited for Benzema's strong form in the first six months of last season.
Now, Zidane has claimed that his countryman could inherit the armband at Los Blancos if he started to 'take the initiative'.
"I'd like it if Karim took the initiative at Real Madrid," Zidane told L'Equipe.
"He's the kind of player that doesn't talk much, but he has both feet on the ground. But he must pass this level in order to become a leader.
"As has happened with the French national team, he could inherit the captain's armband at his club. I hope he rises to the challenge next season. I want Karim to speak to the group rather than have others do it for him."
Benzema is currently with his national team at the World Cup.