Croatia international Kovacic scored his first goals for Inter last week, registering a hat-trick in a trouncing of Stjarnan that ensured the Serie A club cruised into the group stages of UEFA Europa League.
The 20-year-old started only 14 league games for Walter Mazzarri's men last term, but appears likely to play a more prominent role this season.
Having witnessed Kovacic's progression, Juan has tipped his colleague to eventually achieve greatness.
Speaking at Monza, the venue for this weekend's Italian Grand Prix, the Brazilian said: "Kovacic will be one of the world's best in a few years.
"I have great confidence in him and hope he has a great career."
Kovacic also earned praise from Hernanes, who added: "I enjoy playing alongside Mateo but I'm sure we can do even better.
"He is a really talented player. He's got lots of tricks and he reads the game so well."
Inter suffered frustration on the opening weekend of the Serie A season, drawing 0-0 at Torino.
Juan said: "We're not worried. We have lots of games to take Inter to the top. It's important to beat Sassuolo [next Sunday]."
