Velez Sarsfield president Miguel Calello says they've granted Sunderland permission to speak with Peruzzi.
"We talked about the payment conditions and the values, we reached an agreement quickly," Calello told Rock & Pop.
"Now Gino Peruzzi's representatives and the English club need to reach an agreement.
"When this kind of proposal comes, it's hard to say no. If we turn them down, we might never receive this kind of proposal again."