Peruzzi was believed to be nearing a switch to the Premier League after Sunderland had agreed a fee with current club Velez Sarsfield.
However, Velez vice-president Julio Baldomar revealed that the 21-year-old right-back is unhappy with the personal terms offered to him by Sunderland, leaving his future in major doubt.
"The player and his agent say that the offer from Sunderland isn't sufficient - not the transfer fee, because the player will take 15%, which is enough, but what they've offered him," Baldomar told TyC Sports. "They say that isn't it what they want. It's the first time where we've arranged a transfer to a European club and after the player tells us that he wants them to offer more.
"If the player isn't transferred, we have to sit down with the board to see what the next step will be. It's an exceptional case because generally when there appears an offer from Europe, the players is the first person who wants to go. He isn't in agreement with his contract and we cannot do anything about that.
"We need to sit down and think calmly about what we're going to do. If the transfer doesn't go through it causes us delays with wages and payments. And it's not only on the footballing front that it creates problems, but also in the social part of the club, like the school for example, because the subsidies have been reduced by the city council."
Peruzzi is already a full Argentine international having made four appearances for the first team.