Arsenal, however, are still confident that the player will keep his word and join the club.
He claims that Spurs have offered €30m, plus bonuses, which is more than what Arsenal had already agreed with Saint Etienne.
Arsenal had delved deep in negotiations for the €30m rated defender but Saint-Étienne were unable to accept the payment structure suggested by Arsenal.
The news is a huge blow for Arsenal, who have endured a hard summer already in the transfer market.More news: Popular TV show Friends leaves Netflix for new HBO service
Arsenal are also pursuing Celtic left-back Kieran Tierney, 22, and hope to recruit a central midfielder and winger.
Saliba, a France Under-20 worldwide, joined Saint-Etienne in 2016 and is one of the game's most highly-rated young centre-backs.
However, Tottenham have made a last-ditch attempt to secure the services of the France Under-20 worldwide by offering a marginally better deal.
Arsenal face having to give up a higher initial fee in order to beat Spurs, whose offer is all upfront.More news: Tyler Skaggs: Los Angeles Angels throw no-hitter while honoring late teammate
But Spurs, who signed Tanguy Ndombele for a club record £53.8m this summer, have submitted a late bid.
Manchester United have also been linked with the Benfica centre-back, who has a release clause of £54m.
Meanwhile, the Gunners are now in turmoil with skipper Laurent Koscielny about to cop a fine for refusing to go on their pre-season tour.
The Gunners are reluctant to lose Koscielny for nothing and have opened disciplinary proceedings against the want-away defender.More news: Prime Day Preview: New MacBook Air Just $999
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