The Manchester Evening News says City are monitoring the 24-year-old in case they are unable to reach an agreement with Napoli over a fee for Jorginho. Negotiations are ongoing for the Italian international but Kovacic has expressed his desire to join a new club.
"I would like to play more at Real Madrid because I love football and I love being on the pitch," Kovacic told Marca.
"I know that it's difficult to be a starter at Real Madrid, especially when I arrived at a really young age.
"I understand the situation, but because of that I believe the best thing for me would be to go to another club where I'd have the opportunity to play regularly as a starter.
"I think I can have this opportunity and it's one I want right now."