The 23-year-old isn't a key fixture in Los Blancos' strongest XI, with their first-choice midfield typically comprising Casemiro, Luka Modric and Toni Kroos.
Football writer Ryan Baldi noted the former Inter Milan star would enjoy a greater role elsewhere:
Last season, he started 19 matches in La Liga but was still able to showcase his talents.
The Croatia international is an expert at playing his way out of trouble, supremely comfortable in possession and is a robust ball-winner.
According to Squawka, he completed 59 of 82 attempted take-ons in the Spanish top flight last year, maintaining a passing accuracy of 91 per cent and winning 46 tackles.
He also created 17 chances, three of which were converted to assists, and found the net once.
Per the Guardian's Sid Lowe, Kovacic is former manager Rafael Benitez's best enduring legacy at the Santiago Bernabeu:
He would be a superb capture at Anfield, where Liverpool could offer him a starring role. However, despite his status as a squad player in Madrid, he still plays lots of games.
Kovacic made 39 appearances in all competitions last year, and Real boss Zinedine Zidane has shown his willingness to rotate the team to give opportunities to all of his players, so while he'd likely enjoy a greater role than he currently has, he's hardly starved of game time—prising him away will not be so easy.
Meanwhile, Schalke 04 defender Benedikt Howedes has said he would be willing to move abroad amid rumours linking him to Liverpool.
Per Metro's Tom Olver, he said:
"It is clear that I received enquiries from other clubs. It is in the nature of the matter that my advisor checks and answers this. I have always said that I can rule out a move within the league [Bundesliga] and I can imagine a change abroad."
According to DW Sports, Klopp is keen on the Germany international, whose captaincy has been given to another player by new Schalke coach Domenico Tedesco:
Liverpool writer Leanne Prescott believes the Reds should be willing to expand their horizons when it comes to centre-back targets this summer:
Howedes is a versatile operator who can also fill in at full-back or defensive midfield, and he's already capable of slotting in alongside Joel Matip having played with him for years at the Veltins-Arena.
The 29-year-old played every minute of Germany's 2014 FIFA World Cup campaign, too, a feat matched only by Manuel Neuer and Philipp Lahm, so he has plenty of top-level experience to bring to Anfield.
If he's available for the relatively cheap price of €20 million (£18.4 million), he would be a shrewd buy.