The Black Cats were ready to wrap up a deal for the highly-rated Argentine full-back, only to then pull out of a deal after physical examinations offered cause for concern.
Velez have been left bemused by the Black Cats' findings, as they maintain that the 21-year-old is in peak condition.
A ligament problem has forced Sunderland to take a step back, but Coppolecchia is adamant that Peruzzi is fully fit and would be ready to turn out at a competitive level should he return to Velez.
He told Estudio Futbol: "Gino Peruzzi had an injury, it's true, but he is totally recovered and can play.
"In the medical tests they will have analysed everything very carefully, and he is in perfect shape. He has even been playing for the Argentine national side.
"We think it is crazy that Sunderland have blocked him. If he returns to Velez, he can play immediately without any problem because he has done the pre-season work.
"I don't know what happened in England. The injury he had wasn't that serious, it could have been talked over.
"The player is in perfect condition and I don't know what is going to happen from now on."