Lovren has fallen way down the pecking order and is considered the fourth-choice centre-back behind Virgil van Dijk, Joe Gomez and Joel Matip.
The 30-year-old is also standing in the way of Liverpool’s next generation as Ki-Jana Hoever and summer recruit Sepp van den Berg will be given a clear pathway to the first team if the Croatian departs.
Lovren joined the Reds in a £20m deal back in 2014 but injury and inconsistent form has blighted his career on Merseyside.
He was left out of the squad for Liverpool’s Premier League opener against Norwich and has not travelled to Istanbul for the Super Cup clash with Chelsea on Wednesday.
According to the report, Lovren is seeking more first-team action and the club are willing to see his needs met, providing the right offer arrives.
There is cover at centre-back for Liverpool with Fabinho capable of filling in while the two 17-year-old defenders, Hoever and Van den Berg, continue their development.
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