The centre-back's representatives have flown to Italy to initiate discussions for a possible deal, according to Milan News (via The Daily Star).
The Croatian played a bit-part role under Jurgen Klopp last season, making just 18 appearances in all competitions.
Joe Gomez and Joel Matip were favoured to partner Virgil van Dijk at the heart of the Liverpool defence ahead of Lovren and it would appear he is not happy to remain a squad player, despite the success enjoyed by the Reds in 2018/19.
A fee for the 29-year-old is expected to be around the £25m mark.
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