The Black Cats are in "advanced negotiations" with the 21-year-old, according to Velez Sarsfield's vice-president
The 21-year-old, who came through the youth ranks at Velez and has represented his country on four occasions, has previously spoken of his desire to play in the Premier League and now looks to be Paolo Di Canio's first major signing of the summer.
"The negotiations are very advanced," vice-president Julio Baldomar said on TV Publica.
Velez general manager Christian Bassedas has experience of the area after spending three years at Newcastle United from 2000 to 2003 and Peruzzi says positive reviews from his boss has helped make the decision to move away from his homeland.
"It's beautiful, especially since in my opinion it's one of the best leagues because of the tempo played there," Peruzzi told Ole. "I think English football is the most competitive.
"Yes, Bassedas told me about the city, the people, that there is a lot of respect, he said something about the team. He told me that he liked to play there. I want to leave [Velez] as a winner."
Velez were crowned Argentine super champions on Saturday with a victory over Newell's Old Boys.