The England international is expected to leave the South Coast club once he returns from Brazil, with a switch to the Reds having been mooted as the most likely outcome.
But with the Merseysiders understood to be stalling on a move for the playmaker after seeing a ‘take it or leave it’ £25m offer rebuffed before Lallana jetted off with the Three Lions, the situation remains up the air.
Spurs are also keen on the 25-year-old, and now they are confident that they can beat their rivals to his signature.
Although the Lilywhites do not boast Champions League football for next term, Mauricio Pochettino’s presence may be key.
The Argentine left the Saints a few weeks ago to join Tottenham, and is known to have a good working relationship with Lallana.
Chairman Daniel Levy is thought to be willing to use this and pay big to land the silky passer, who could become the focal point of Spurs’ first XI as they look to mount a fresh top four challenge.
Jay Rodriguez is also a target for the Lilywhites.