Velez Sarsfield said on Wednesday that the 21-year-old would fly to Wearside on Thursday to finalise the transfer.
However, they released a statement on their official website confirming that he will not now travel until the weekend.
It said: "Given the imminent transfer of Gino Peruzzi to Sunderland Association Football Club, finally next Sunday, July 14, both the player and the directors Julio Baldomar and Eduardo Ordonez will travel to England to complete initial contracts between the parties and thus close the sale."
The Black Cats are also closing in on Juventus' Italy international midfielder Emanuele Giaccherini with manager Antonio Conte having told reporters he is leaving to help ease the financial burden on the club.
- Sports & Recreation