The Argentine outfit confirmed in a statement on their official website that the player had not passed his initial examination at the Premier League side.
He was found to have an issue with his knee ligaments, which were initially damaged during a Copa Argentina defeat to Olimpo in April.
The move now hinges on whether the Argentinian passes a second medical due to take place at the Villa Stuart Sport Clinic in Rome.
The 21-year-old had agreed in principle to join the club, with Sarsfield general managers Julio Baldomar and Eduardo Ordonez having travelled to England to further the negotiations.
Sunderland manager Paolo Di Canio has been busy re-shaping his squad during the close-season, as he looks to build on a 17th-place finish during the previous campaign.
Peruzzi would become Di Canio’s 10th signing of the transfer window, joining the likes of Jozy Altidore, Modibo Diakite and Emanuele Giaccherini in making the switch to the Stadium of Light.
