The 29-year-old defender believes his team-mate can become one of the best in the world and says los Blancos need to work as a team in order to beat Barcelona on Tuesday
The French youngster has garnered acclaim having produced a series of domineering displays at the heart of los Blancos defence in 2013.
And Pepe has revealed he is helping the 19-year-old to ready himself for global success.
Speaking to AS, the 29-year-old said: "He is a very humble guy but he has tremendous quality. At the start of the season, I told him that within two years, he will be one of the best centre-backs in the world.
"I hope he continues with his humility and eagerness to learn because he is already doing so well. I think he can really progress and all of this experience he is getting can only be good for him."
Varane starred in Real's 1-1 draw with Barcelona in the Copa Del Rey last month and, speaking ahead of Tuesday's second leg, Pepe believes progression to the final hinges on the team operating as a unit.
He added: "We need to play as a team, like we try to do in every game.
"If we play that way, we will be in with a good chance of making the final. Playing collectively will boost our chances of winning. We need to remain true to our style of play and do everything the coach tells us to do."