The 27-year-old centre-half was instrumental in the Spanish club’s Europa League triumph last season, captaining the side whilst making 38 appearances in all competitions.
Fazio, capped twice for Argentina, more recently produced a superb display in the UEFA Super Cup final defeat to Real Madrid and Spurs have now turned their attention towards him after problems emerged over a deal for Villarreal centre-back and fellow Argentinian Mateo Musacchio.
Sky Sports reported earlier this month that Tottenham had opened talks with Villarreal over Musacchio, 23, but those discussions reached an impasse with the player’s third-party ownership.
And a deal for Fazio may already be progressing more soundly after Sevilla manager Unai Emery strongly suggested on Friday that Tottenham have already met the player’s £8million release clause.
Emery, whose side play Valencia in their opening La Liga fixture on Saturday, said: “Federico belongs to our staff but he has little or no chance of playing for us tomorrow.
“We cannot deny the fact he gave a very high level of performance in his last game, the Super Cup, which was instrumental in teams being interested.
“Clearly we would all prefer him to stay, but thinking about tomorrow's game we will have to look elsewhere. The player has constantly given his all to Sevilla. It remains only that we wish him well.
“When I arrived he was criticised as a player and about to leave for an amount much lower than this. But he has grown so much, and in his renewed contract his price was set far above what was previously offered for him.
“But his performances have been so high that he has outgrown that clause. Fazio is worth more than that, but those are the rules of the game."
Fazio joined Sevilla from Buenos Aires-based club Ferro Carril Oeste in 2007 and has made almost 150 appearances for the club.