Zidane has helped Benzema fulfil his potential at Real over the past 12 months.
"I would like Karim to take the initiative at Madrid," the 41-year-old assistant coach said.
"He's the kind of player who doesn't talk much but he has his feet on the ground. He must move up a level to become a leader.
"As in the France team, he can inherit the captain's armband with his club.
"I hope he meets the challenge next season. Karim can talk to the group, rather than have others do it for him."
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