Gazzetta dello Sport writes on Thursday that the two clubs are still locked in talks over the structure of a deal that could see the Croatian leave Anfield after five years on Merseyside.
An agreement is yet to be reached as Liverpool hold out for a €20 million transfer fee.
Roma are offering €3 million up front for an initial loan, with the obligation to make the move permanent in a year’s time set at €12 million - although this clause would be linked to how many appearances the centre-back makes.
The Giallorossi could compromise and raise the future fee to around €15 million for a deal worth around €15-18 million in total.
Lovren played 18 matches in all competitions for last season's Champions League winners Liverpool.
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