The highly rated 17-year-old is a regular in Dinamo's side and has even captained them before.
His performances have attracted the interest of several club across Europe including Juve although Barclays Premier League side Arsenal are believed to be the only side which have submitted a formal bid for the player so far
The Austrian-born Croatian Under-21 international is now reportedly also a target for Manchester United but it seems Kovacic is happy enough to continue his football education in Zagreb.
"There are many talks, every footballer is dreaming of playing for one of the best clubs in the world but I'm not really bothered what is going on in press," he told SportskeNovosti.
"There are many rumours, but I'm happy to stay at Dinamo.
"I'm still young and I still have to learn before I will be ready to move on.
"It is nice to see your name linked with clubs such as Juventus and Manchester United, but I'm quite calm. My time will come sooner or later."
Meanwhile, Juve manager Antonio Conte has reiterated his desire to keep winger Milos Krasic at the club despite speculation linking the player with a move away from Turin.
The 26-year-old has started in only one of Juve's matches this season, Wednesday's 1-1 draw against Bolgna, after a disappointing finish to the previous campaign.