The Croatia international fell out of favour at Anfield last term, with Virgil van Dijk, Joe Gomez and Joel Matip now ahead of him in the centre-back pecking order.
Lovren is keen to leave the club and get more regular first-team minutes elsewhere.
And Roma appear to have won the race for his signature, with the Italian side poised to complete a deal worth up to £23m.
Lovren was left out of Liverpool's squad for the Super Cup victory over Chelsea on Wednesday as talks about his future intensified.
And the former Southampton man is edging closer to the exit door after five years on Merseyside.
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