Velez have accepted a bid from Sunderland for the Argentine.
Peruzzi, 21, said: "There was an agreement between both teams, but I had to analyse my contract. Together with my family we decided that it wasn't what we expected and that's why we said no.
"It's not that I don't want to go to Sunderland - it's a team in the Premier League, one of the most important leagues in Europe. I am willing to listen to a new proposal."