Peruzzi is due to feature for Velez against Newell's Old Boys in the Argentine league final at the weekend and he insists he is concentrating on that game.
However, the 21-year-old international, who has four caps for Argentina, is reportedly the subject of a bid from Wearside.
Peruzzi, the cousin of former Italian international Angelo Peruzzi, came to the fore in the 2012 Copa Libertadores when he brilliantly marked Neymar out of their semi-final clash with Santos.
The player himself is reported to have confirmed the offer from Sunderland but said: "My mind is set on Newell's, and then we will see."
Velez's general manager is, somewhat ironically, former Newcastle midfielder Christian Bassedas, who admitted Peruzzi was set to leave.
"He is the one that is closer to leaving the club," he told Ole.
Due to his Italian family, Peruzzi would be able to secure a European passport, meaning he would not require a work permit to play in the Premier League.