The Saints centre-back is understood to be ready to leave the South Coast club after just one season, and has been heavily linked with the Reds in recent weeks.
But Spurs boss Mauricio Pochettino is keen to ensure that the 24-year-old follows him from Hampshire to north London.
The Argentine coached Lovren while at St Mary’s Stadium and is known to be a huge admirer of his talents.
Liverpool were thought to have considered themselves as the best option for the defender, but Pochettino is hopeful that his relationship with the player will win out.
Whereas the Merseysiders have Champions League football to offer, Spurs can only present Europa League action, but the Croatian may face an easier task in becoming a regular starter at White Hart Lane.
Southampton want £15m for Lovren in what could be a massive sell off at the club with Adam Lallana, Luke Shaw and Jay Rodriguez among other looking likely to follow Rickie Lambert – who has joined Liverpool – out of the exit door.