It was revealed on Monday that the 21-year-old Argentine has turned down the chance to join the Black Cats due to an issue over personal terms.
"There was an agreement between both teams but I had to analyse my contract," Sky Sports News quotes Peruzzi as saying. "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."
Peruzzi signed his first professional deal with Velez in 2010.