The 18-year-old has already agreed terms with the Gunners and was all set to sign a five-year deal before being loaned back next season.
But Spurs have been monitoring developments over the last few weeks and are ready to blow Arsenal’s offer out of the water.
They have more money to spend after their run to the Champions League final, while Unai Emery’s transfer budget is restricted after his side’s loss in the Europa League final.
Arsenal have agreed a payment structure with Saint-Etienne, which involved paying most of the fee for Saliba next summer.
But Spurs have told the Ligue 1 side they are willing to offer a bigger slice of the fee up front and they too are willing to send him back on loan next season.
It is also understood Tottenham have offered better add-ons if Saliba hits a number of targets with them.
France Under-20 star Saliba must now choose where his future lies – leaving Arsenal sweating on his decision.
Meanwhile, the Gunners are currently in turmoil with skipper Laurent Koscielny about to cop a fine for refusing to go on their pre-season tour.
He wants to be allowed to leave the club on a free despite having one year left on his contract, with Rennes pushing hardest to sign him.
But Arsenal are desperate to raise cash from sales to reinvest in the squad and want £8.9m for him, with the club willing to dig in their heels.
Spurs also have issues in defence with Toby Alderweireld’s £25m release clause currently active and Roma closing in on the Belgium star.
At one point it looked as though the Serie A giants had shelved their interest – but a deal is now back on the cards after high-level talks yesterday.
Spurs are interested in highly-rated Italy midfielder Nicolo Zaniolo and Roma could include him in any deal for Alderweireld.