Liverpool were keen on the midfielder before his move to Real Madrid last year.
Real Madrid's Mateo Kovacic (L) in action against Shakhtar Donetsk's Fred
Liverpool are expected to be busy in this summer transfer window as Jurgen Klopp looks to better mould the squad to suit his plans.
Several areas of their squad are likely to be strengthened, with midfield one area he may look at.
Lucas Leiva, Joe Allen and potentially even Jordan Henderson may join Jordan Rossiter in leaving and should that happen, reinforcements would be needed.
There are several options they could explore, but a return for Kovacic would be a wise one.
Liverpool manager Jurgen Klopp with James Milner during the warm up before the match
Liverpool were heavily linked with the midfielder last summer before he eventually made a move to Real Madrid.
His time in Spain has not been good, with just 34 appearances in all competitions, 22 of which were as a substitute.
At Liverpool though, he would be easily challenge for a first team place. He would certainly represent an upgrade on both Jordan Henderson and James Milner.
He could slot in nicely alongside Emre Can in the Reds midfield, with the German offering the defensive protection and Kovacic the passing ability the midfield is currently lacking.
Liverpool have been lacking someone with that kind of passing range since Steven Gerrard’s departure and the Croatian could be a viable long-term replacement for their former captain.
Liverpool's Steven Gerrard celebrates with Liverpool manager Brendan Rodgers
At just 22-years-old he also fits perfectly into Klopp’s policy of buying young to develop for the future, and he could mature well under the German’s leadership.
He has a strong history of developing midfielders, Ilkay Gundogan and Mario Gotze are chief among his success stories, and Kovacic could add himself to that list.
Of course, much would depend on who leaves Liverpool this summer, but if there are several exits, then they should revive their interest in Kovacic.
Shakhtar Donetsk's Vasyl Kobin in action against Real Madrid's Mateo Kovacic