According to the Metro, Lovren will go on strike in an attempt to secure his transfer to Liverpool after the Reds had a £20m offer for the player rejected by Saints.
If successful, Lovren will be the third Saints player to join the Anfield club this summer, after Rickie Lambert and Adam Lallana signed for the Reds. But Arsenal and Spurs are waiting in the wings should Liverpool talks stall.
The report claims Liverpool submitted a £20m bid for Lovren shortly after completing the £25m transfer of Lallana. Saints signed the Croatian international, who crashed out at the group stage with his country at the World Cup, for £8m from Lyon last summer.
Despite the opportunity to more than double their money on the defender in 12 months, Southampton's board is eager to make sure that Lallana is the last big name to depart. Luke Shaw was another to leave St Mary's, in a £27m deal to Manchester United.
Even before the World Cup, Lovren handed in a transfer request to Southampton, making it clear that he sees his future elsewhere next season.
The 24-year-old has been linked with a move to Tottenham, where he would get the opportunity to play under former-Saints boss Mauricio Pochettino again. But it looks like Liverpool are the heavy favourites to win the race, as they're the only team to have made a solid offer so far.
Performances last season
Using statistics taken from whoscored.com, Lovren was Southampton's best player last season. He made 31 Premier League appearances last season, scoring two goals, including the winner against Liverpool at Anfield.
He formed an excellent defensive partnership with Jose Fonte at St Mary's, and Brendan Rodgers has identified him as the perfect addition to a Liverpool back-line that looked shaky at times.