The Croatian could be set to leave the Bernabeu if Andre Gomes arrvies from Valencia.
The Reds are expected to be busy this summer as manager Jurgen Klopp builds a squad to better suit his needs.
He has already made five signings with Marko Grujic, Joel Matip, Loris Karius, Sadio Mane and Ragnar Klavan all making the move to Anfield.
More signings are likely though and according to Marca they still have an interest in Kovacic.
The Croatian midfielder has long been linked with a move to Anfield, even before Klopp’s arrival, and the Spanish publication claims that interest has not waned.
He has struggled to make an impact at the Bernabeu since arriving from Inter Milan, with both Rafa Benitez and Zinedine Zidane failing to find a role for him.
Real are now allegedly looking to sign Andre Gomes from Valencia and should he arrive Madrid will listen to offers for Kovacic this summer.
The player is keen to try to prove himself with the La Liga giants, but with first-team football hard to come by perhaps an offer from Liverpool would be tempting.
They are not the only ones interested in his services though, with Marca claiming that several sides in Italy are also keen.