The Austrian moved from Inter Milan in 2015 and has mostly been given bench roles.
Kovacic said: “I would like to play more at Madrid because I love football and being on the field of play. And I know that at Madrid it’s difficult to play as a starter, especially because I arrived [here] very young.
“I understand the situation, but that is why I think that the best thing for me is that I go to another club where I have the opportunity to play regularly as a starter.
“It’s an opportunity that I think that I can have and that I want right now.”