The 21-year-old is reported to have snubbed the chance to join Paolo Di Canio's side after the two parties struggled to agree personal terms.
|5/1||Sunderland are 5/1 with Paddy Power to be relegated next season
He told Radio La Red: “My intention is to keep negotiating my contract with Sunderland. If they improve their offer, I won't rule it out.”
Peruzzi has made four international caps for Argentina and has previously been linked with a move to Serie A giants Inter.
Sunderland boss Di Canio has already been busy in the transfer market adding a number of new players, including Modibo Diakite, Cabral and Vito Mannone.