They have been linked with Marco Giampaolo, the...
29-year-old Lovren is under contract at Anfield until 2021.
The Croatia global moved to Anfield for £20million (BBC) back in 2014, but could soon have the option to move to the San Siro.
Last season, the Croatian worldwide defender only made 18 appearances for Liverpool in all competitions.
However, Press Association Sport understands Liverpool are in no rush to usher Lovren, 30 next month, out of the door and it would take an offer of at least £25million to persuade them to change that stance.
However, the reporter has indicated that Milan's interest appears to genuine.
It is claimed the Rossoneri are yet to approach Liverpool to even enquire about Lovren and therefore, no concrete negotiations are under way at the moment.
Frederic Massara is believed to be taking over as Milan's new sporting director after Leonardo left for PSG.