Fazio, who was born in Buenos Aires, has represented Argentina at the 2008 Olympic Games and in three friendlies but has yet to make an appearance for them in an official international fixture.
The 29-year-old's grandfather came from Sicily and he said that, having given up hope of a call-up from Alejandro Sabella, he could opt to play for Italy if Giampiero Ventura asked him to.
He told Ultimo Uomo magazine: "I was a regular at Sevilla, a recognised player in Spain, and I felt I was in form and I would have liked to have had at least a chance.
"But since Sabella has been in charge, this chance has never come. It's a lack of respect. I'm sorry that I was never given a chance to show my value.