The 21-year-old Croatian international moved to the San Siro three years ago but enjoyed by far his most effective campaign in 2014/15 and is now the subject of intense interest both in Italy and England.
Brendan Rodgers saw Steven Gerrard leave for Major League Soccer outfit Los Angeles Galaxy over the summer, and Kovacic could potentially offer the Liverpool manager a cultured central midfield option, going some way to replacing the departed Merseyside great.
The Gazzetta claim that Liverpool have failed with an earlier bid of €25m (£17.7m), and that Inter Milan want €30m (£21.3m) for the former Dinamo Zagreb man.
Inter would face the wrath of their home supporters if they considered selling to AC Milan, and Roberto Mancini would be loath to lose Kovacic, who made 44 appearances in all competitions last season.
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Kovacic is a creative midfield talent who also has the steel to effectively fill a holding role. He is incredibly comfortable on the ball, and has the attributes that would well suit Rodgers.
However, despite Gerrard’s departure, Liverpool have considerable options in the heart of the midfield, and Kovacic would have to compete with the likes of Jordan Henderson, Emre Can, Joe Allen, James Milner and Lucas Leiva for a starting berth.