Arsene Wenger has an interest in bringing the young midfielder to the Premier League according to Zagreb director of sport Zoran Mamic.
The 17-year-old has been the subject of much transfer speculation in Croatia this summer after impressing in the latter half of last season.
The youngster has attracted attention from Ajax, Bayern Munich and Juventus as well as the Gunners.
However Mamic believes Kovacic is out of Arsene Wenger’s price range if they decide to cash in on the young starlet.
"A few days ago I talked with some of my friends from Arsenal," he told 24sata. "I told them that Mateo is in good form, that he is playing good.
"They said that is very good for us, but bad for them. They say that Arsenal can't join this 'dance of millions' for him.
"They rate Kovacic very highly but are also afraid that he will be too expensive for them soon."
Kovacic has only managed eight first team games for Zagreb so far in his fledgling career but has managed to find twice in the period.