Liverpool signed Lovren from Southampton for £20m in July 2014 and he has since helped the club win both the Champions League and Premier League under Jurgen Klopp.
However, the 31-year-old has found his first-team opportunities limited in recent seasons, with Virgil van Dijk, Joe Gomez and Joel Matip largely preferred in central defence. This season he was limited to 15 appearances in all competitions.
Liverpool are willing to let Lovren leave and it is now up to Croatian international to decide if he wants to join Zenit and to agree personal terms with the Russian club.
Lovren has just one year remaining on his current deal at Anfield but Liverpool have an option to extend his contract for another season, if he remains at the club at the end of the summer transfer window.