The Croatia international has slipped down the centre-back pecking order at Anfield and looks set to depart in the coming weeks.
Although the Premier League transfer window closed on Thursday, European clubs are still able to buy new players until the end of August.
And Roma are keen to land Lovren on a loan deal with an option to buy for around £18.8m.
The Giallorossi have identified the former Southampton stopper as a potential replacement for Kostas Manolas, who has joined Napoli.
Lovren has made 170 appearances for the Reds since joining the club in 2014.
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