The Croatian is now the fourth-choice centre-back at the club, and Liverpool are happy for him to move on if their asking price is met.
Lovren has previously attracted interest from Roma, but the current financial climate looks to have scuppered any hopes of a permanent transfer in the coming months.
The 31-year-old is valued at around £15million by his employers, who are not willing to drop their price tag despite the current financial circumstances.
Now Sky Sports report Liverpool could even take up their option to keep Lovren at the club a further year, by extending his current deal to 2022.
Lovren has made 185 appearances for Liverpool since costing them £20million from Southampton back in 2014, though has played a more bit-part role over the last two seasons.
He impressed when deputising in the Premier League win over Leicester at Anfield earlier this season, though had a nightmare evening in the Reds’ disappointing 3-0 loss to Watford – which signalled the end of their unbeaten run.
Russian outfit Zenit St. Petersburg have been showing interest in his services of late, but Liverpool boss Jurgen Klopp insists he still has a part to play next season.
“Dejan has played outstanding games for us,” said Klopp. “He is a very important part of the squad. We have four centre-halves and we play usually with two of them, but we have needed all four – always.
“There is a value to his experience, absolutely. Since I’ve been in here, Dejan was always either in the team, close to the team or not available. There was never anything else, we have never had any problems.
“There is nothing to discuss in public about his contract situation. The situation is absolutely clear – Dejan is a player of LFC and we need him.”
The move is more likely to be a strategy to avoid losing Lovren for nothing when his contract expires next year though, rather than a reward for his contribution to the team.
It is believed Liverpool are still open to selling Lovren if they receive the right offer, but finding a replacement in the uncertain market could prove challenging.
Klopp is blooding youngsters Sepp van den Berg and Ki-Jana Hoever for first-team roles in the long term, while Nat Phillips has returned from his loan at Stuttgart, but none are thought to be deemed ready to step up for use as back-up.
Joel Matip is also currently out injured, while Joe Gomez has had a number of fitness problems in recent seasons, meaning Lovren will not be let go without someone arriving in his place.
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