Tottenham had lined up a €21 million move for Villarreal centre-back Mateo Musacchio but have turned to Fazio after third-party issues complicated their pursuit of the 23-year-old.
And Emery has now confirmed that Fazio is set to depart Ramon Sanchez Pijuan after seven years - for a fee matching his reported €10 million release clause - having made just under 200 appearances for the club.
"I have followed Fazio's evolution for a year and a half. When I arrived he was criticised," he said.
"In a year and a half he has grown tremendously and his release clause has stayed low, but that's football. Fazio is worth much more than that. We all feel sad that he is leaving."
However, Emery conceded that he would have liked to have retained the services of the 27-year-old, admitting: "He was our captain, his evolution has been incredible up until the last game that he played and this has attracted other clubs.
"If he goes it will be for the release clause in his contract but we would prefer it that he does not go. We wish him the best, we will want to replace him."
Should Fazio join Spurs he will become their fourth defensive signing of the summer, following the arrivals of Eric Dier, Ben Davies and goalkeeper Michel Vorm.