According to Jamie Sanderson of Metro, the player has been dropped in recent weeks despite some good performances. Rumours of a falling out with manager Walter Mazzarri have surfaced, but the player's agent noted:
"Everybody is confused as to why Mateo is not playing. Is there a row with Mazzarri I can’t say a lot, but he is not happy."
The news that one of Europe's hot young properties may therefore become available has alerted the eagle-eyed and studious Rodgers.
Liverpool have been long-term admirers of the 19-year-old who has made an excellent impact in Italy since his transfer from Dinamo Zagreb.
As Steven Gerrard begins to wind down his Liverpool career, Rodgers needs someone alongside Jordan Henderson who can take a game by the scruff of the neck and influence proceedings.
Despite his young age, Kovacic is that man.
Dynamic, energetic and with a wonderful passing range, the Croatian is akin to Gerrard in his pomp and could be another masterful signing from Rodgers as he begins to build on a successful season.
Croatian football journalist Aleksandar Holiga certainly thinks it would be a good move:
If the fee being quoted is accurate, then it's fully understandable why the Liverpool manager is keen to see off competition from Manchester United, Chelsea, Arsenal and Tottenham and conclude a deal for the player before the World Cup.
Whilst Coutinho has the lowest pass success rate of those mentioned, there is no doubting the Brazilian's impact at Anfield.
His passing is intelligent, sharp and incisive, and Rodgers himself said of Coutinho just after his transfer, per Liam Twomey of Goal.com:
We are all pleasantly pleased and surprised by how well he has done. His numbers tell you the story in terms of goals and assists.
At the minute, you can't ask any more. The key thing is that he works his socks off as well. He is a real team player.
[...] He's been a real find for us in terms of the price we paid.
It would be that sort of impact that the Northern Irishman will be looking for from Kovacic, and if his time in Italy is a guide, then Rodgers is unlikely to be disappointed. Indeed, Kovacic was the replacement for Coutinho when the latter left for Liverpool.
He [Kovacic] has the potential to become better than me. He's a serious professional. He's not a born playmaker. He's not yet a complete player. He has to work but he has football in his blood. He is very fast ... quick. Inter have done well to sign him. He can play either on the left or right of central midfield in a 4-3-3 or a 3-5-2. He could also become a playmaker in a few years' time.
Amid such high praise, one has to ask the question why he has gone from being a regular in Andrea Stramaccioni's side to an also-ran for Mazzarri. Of course rumours of coaches and players not getting along is commonplace.
But Inter's loss could very well be Liverpool's gain.
Kovacic always looks comfortable on the ball and appears happiest when in possession of the football.
A workaholic midfielder, he doesn't wait for the ball to reach his feet. If he wants to affect the play, he goes foraging. Manna-from-heaven in a Rodgers setup.
Superb acceleration from a standing start will take him away from the opposition, and his drive and powerful forward runs will delight the Anfield faithful whilst striking fear into opposing defences.
Add to that, great vision and an ability to switch left or right with ease, Kovacic is a truly emerging talent.
And one that would fit in perfectly on the red half of Merseyside.