Liverpool are reportedly keen on a move for the Real Madrid midfielder.
Real Madrid's Mateo Kovacic (L) in action against Shakhtar Donetsk's Fred
The Croatian is far down the pecking order at the Bernabeu having failed to break into their highly talented midfield since joining last summer.
Shakhtar Donetsk's Vasyl Kobin in action against Real Madrid's Mateo Kovacic
He managed just eight starts in La Liga last season, with neither Rafa Benitez nor Zinedine Zidane handing him a starting role in the team.
That has sparked suggestions that a return to Italy could be on the cards this summer to bring an end to a short and unsuccessful spell in Spain for him.
However, it appears that he may have another potential destination to consider, with Gianluca di Marzio claiming Liverpool are interested in him also.
Real Madrid's James Rodriguez, Mateo Kovacic, Gareth Bale, Luka Modric and Raphael Varane celebrate with fans after the game
According to them, manager Jurgen Klopp is bewitched by the midfielder and is keen to make a move to try and sign him.
They would make a permanent move for his services rather than a loan bid, which could convince the European champions into a sale.
A price is not named for the player, although it would likely be around the £21million price tag that was touted by the Telegraph last year.
Liverpool manager Juergen Klopp