Benzema was part of the Los Blancos side that won the Champions League and Copa del Rey last season, but was overshadowed by Gareth Bale and Cristiano Ronaldo's displays as they clinched La Decima - their 10th European Cup win against local rivals Atletico Madrid.
The France international has netted 112 goals for the La LIga giants since making his £30 million switch from Lyon in 2009, but Zidane wants to see his compatriot seize the intiative next term.
The World Cup winner, who is assistant to Carlo Ancelotti at Santiago Bernabeu, thinks that there is plenty of room for improvement from the Les Bleus hitman.
Zidane told reporters: "I hope he meets the challenge next season. Karim can talk to the group, rather than have others do it for him.
"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 would like Karim to take the initiative at Madrid."
Benzema is likely to be named in the starting lineup for France's clash with Honduras on Sunday evening, as Didier Deschamps' side begin their World Cup campaign in Brazil.