Lovren fell down the centre-back pecking order last term and is currently fourth choice behind Virgil van Dijk, Joe Gomez and Joel Matip.
The former Southampton stopper has two years remaining on his Liverpool contract and is open to a departure in the next 10 days.
Lovren was left out of Liverpool's matchday squad for Friday's 4-1 victory over Norwich.
Jurgen Klopp's side will take on Chelsea in the UEFA Super Cup on Wednesday, but Lovren is not expected to play a part.
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