The 23-year-old has largely impressed since arriving at the club from Dinamo Zagreb, and he is tipped to leave Stade Gerland for greener pastures in the summer.
Lyon find themselves in a very difficult situation and president Jean-Michel Aulas has earlier revealed that the club will be forced to sell at least two star players at the end of the season.
Dejan Lovren is wanted by AC Milan, who have yet to sign a proper replacement for Thiago Silva, and they believe the Croat would be a great addition to the squad at San Siro.
Liverpool, Inter Milan, Rubin Kazan and Lokomotiv Moscow are also showing interest in the highly rated defender.
Dejan Lovren joined les Gones in an €8 million deal from Dinamo Zagreb in January 2010 and has since made 70 Ligue 1 appearances for the club.