The Saints centre-back is widely expected to become the fourth big name star to leave St Mary’s Stadium this summer, with Liverpool having been mooted as his most likely destination.
Rumours last week suggested that the Reds offered £20m for the Croatian and with the fee understood to have matched an agreement between the player and the club allowing him to leave after a transfer request was made, the South Coast outfit’s decision to reject has been met with anger.
The 24-year-old is understood to be ready to refuse to go back to the club for pre-season training, which has alerted Mauricio Pochettino.
The Argentine – another name to have left the Hampshire side – managed Lovren last term, and is known to be a big fan of his abilities.
With Liverpool distracted by the Luis Suarez episode, Spurs are hopeful that they can sneak in with an £18m-£20m offer and nab the defender.
Adam Lallana, Rickie Lambert and Luke Shaw have already left Southampton in recent weeks for over £60m.