The 21-year-old Argentina international is understood to have been identified as a transfer target by Sunderland as manager Paolo Di Canio looks to reshape his squad ahead of the new Premier League campaign.
Velez vice-president Julio Baldomar says the two clubs are in discussions and has indicated that confirmation of a transfer could be imminent.
"The negotiations are very advanced," he said on TV Publica.
Peruzzi, who can also play on the wing but is primarily a right-back, would welcome a move to the Premier League and has spoken to Velez general manager Christian Bassedas, a former Newcastle United player, about life in the North East of England.
"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."