Zidane, regarded by many as a legend of the game, has been impressed with Benzema's recent form, which included a goal against former club Lyon in the Champions League on Tuesday evening.
Benzema originally arrived at the Santiago Bernabeu in the summer of 2009 but had to make do with a reserve role in his first season at the club, scoring just nine goals in 33 appearances.
That seemed to be the case early on last season, although an injury to first-choice striker Gonzalo Higuain then presented Benzema with a chance, which he capitalised on, ending the campaign with 26 goals in 48 games.
And having already bagged six goals this season, Zidane, who is now working at Real as a sporting director, believes Benzema is doing all he can to stake his claim to a place in Real's starting eleven.
"He knows that there is extra pressure to perform, because we have another striker [Higuain] who knows how to score as well," said Zidane, according to RTL.
"He has responded very well though."
And Zidane believes Benzema has matured as a player since arriving at the Bernabeu.
"He has a lot of quality and has really grown.
"His good performances are the result of hard work and are not a coincidence."
Benzema has also been capped by France 40 times, and has notched up 13 goals along the way.