Injuries have played a big part in limiting Lovren to just nine Premier League appearances this season, but he has been benched in favour of Joel Matip in recent weeks, while Joe Gomez remains Jurgen Klopp's preferred partner to Virgil van Dijk when everyone is fit.
Lovren hasn't been able to take advantage of the injured Gomez's absence and the Daily Mirror claims Napoli and Roma in particular are looking at the 29-year-old as a result of the ongoing interest in their own defenders.
Kalidou Koulibaly and Kostas Manolas have both been the subject of much speculation in recent weeks, with Manchester United heavily linked with both. Juventus and Real Madrid are said to be eyeing Koulibaly, while Arsenal have also been mentioned in relation to Manolas.
The Mirror also notes interest in Lovren from Milan, but no further detail is offered.
Having seriously bolstered their defensive ranks with the £142m acquisition of Van Dijk and goalkeeper Alisson, Liverpool could yet further strengthen at the back this summer.
The Reds have suddenly been linked with Real Madrid and France star Raphael Varane after recent reports that he is looking to leave the Bernabeu in search of a new challenge.
But a big overall Liverpool spend this summer seems unlikely after ploughing around £250m into the transfer market in the last 18 months alone.
Klopp played down suggestions of major investment earlier this month when he said, "there's no need for that level," in response to questions about repeating last summer's £170m spend.
Source : 90min