Manager Antonio Conte has already signed four players as he looks to build a squad capable of challenging Manchester City and Liverpool at the top of the Premier League table.
Moves for Richarlison, Ivan Perisic, Yves Bissouma, and Fraser Forster have all been completed, with Middlesbrough's Djed Spence also close to joining.
And there could be two more in the pipeline, according to the Mirror.
A deal to sign Barcelona's Clement Lenglet has reportedly been close for a while, with the Frenchman set to join on an initial season-long loan.
But Spurs are said to be keen on another centre-back from Spain's top-flight, with Villarreal's Pau Torres - heavily linked with Man United last season - on their radar.
It's now claimed they could go back in for the 25-year-old, with Giovani Lo Celso potentially used as a makeweight in the deal.
The Spurs players have returned to pre-season training this week, but whether the Argentine remains with the group for their tour of Korea remains to be seen.
The pair would join Cristian Romero, Eric Dier, Ben Davies, Davinson Sanchez, Joe Rodon, and Japhet Tanganga as defensive options at the club.
And the addition of Lenglet and Torres may allow Rodon to leave the club on loan this summer.