The Daily Mail says Zenit are willing to offer around £9million for Lovren.
The centre back has been earmarked as a potential replacement for Branislav Ivanovic and is understood to be open to the move with the prospect of playing first team football more regularly.
The 31-year old has one year left on contract though Liverpool have indicated they will take up their option to extend that by another year if he remains with them at the end of the summer.
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