The France Under-21 international only arrived in the Spanish capital from Lens last summer but he is already being tipped for greatness after impressing during his six La Liga appearances to date for Los Blancos.
However, Varane feels it far too early for talk of him emulating the achievements of Zidane at the Santiago Bernabeu.
"I can not compare with Zizou," the 18-year-old defender is quoted as saying by his club's official webiste. "He is a legend.
"I am a young player at Real Madrid. I came here to help the team and to progress in my career. The goal is to grow as a person and player.
"It's a fantastic team with great facilities; a huge club. I've only seen amazing things so far."
Varane is also remaining grounded in terms of Madrid's title challenge, with Los Blancos currently 10 points clear of second-placed Barcelona at the top of La Liga.
"There are still many games and we have to work very hard to achieve it [the title]," he stated.
"[But] the team has defended well and are in solidarity with one another. It is important to defend well to win."
Varane has made 11 appearances for Madrid in all competitions so far this season and has yet to give away a single foul.
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