Real Madrid have turned down a bid of €75m from Serie A Champions Juventus, according to Spanish publication AS.
The Italian club reportedly made the offer at some point in the last few days, but were informed by Real Madrid that the player is not for sale at any price.
After confirming the arrival of Blaise Matuidi from Paris Saint-Germain on Friday, Juventus are not expected to continue their attempts to sign Kovacic.
The Croatian playmaker has emerged as an important part of coach Zinedine Zidane's squad, impressing in Los Blancos' convincing 5-1 aggregate win over Barcelona in the Spanish Super Cup.
Zidane praised Kovacic's "great display" in the first leg victory at the Nou Camp, and it appears that he could be set for more regular game time this season.
Since joining Real Madrid for €31m from Inter in the summer of 2015, the 23-year-old has made 75 appearances in all competitions, scoring three goals.
Kovacic initially struggled to break into the first team following his arrival from Italy, but he has been one of the beneficiaries of Zidane's rotation policy.
The Frenchman utilised his squad to great effect last season as Real Madrid won La Liga and the Champions League, often using a second string side for more winnable league fixtures.
Kovacic has been part of that, but has demonstrated in the early weeks of this campaign that he could step up as a regular in Zidane's favoured starting lineup.