After starring at the 2018 World Cup, the midfielder has attracted interest from Inter Milan, who have reportedly offered a contract worth €10m-a-year.
The Croatian wants to speak with the club and new coach Julen Lopetegui when the squad returns from their USA tour.
And he may not be the only Croatian on his way out of the club, with Luka Modric due for showdown talks with Real President Florentino Perez tomorrow.
It follows Cristiano Ronaldo swapping the Spanish capital for Italy after agreeing a move to Juventus following a trophy-laden spell at the Bernabeu.
It seems that the ball is now in Real Madrid's court.
"As for Modric, there's nothing more for me to add". "We're in no doubt at all that Modric is going to continue playing for us just as he has been".
Lopetegui can not understand the demands Kovacic has made, having been told by the player in their July talks that only a guaranteed starting spot would convince him to stay. He'll be happy with the proposal he receives here.
As for Chelsea, he could be a good signing, and with the player also hungry for success, it could be a win-win situation for all three parties.
"If he leaves, we will have to look for a player of his level, because we want a balanced team". "Gareth Bale is obviously a great player but it's not for me to make comparisons".