The Argentine full-back was due to become the Black Cats' tenth signing of the summer before he failed a medical last week.
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"At the moment, there is no chance for Gino Peruzzi to join us," Di Canio told reporters.
"We have to make sure about some situations but my club is not a club that can sign at the moment a player who is injured, even though it's not a crucial injury.
"We are not Manchester City, who can think about buying a talented player with an injury and wait for him.
"We are not very late [in the transfer window], but I would like a player ready to join the rest of the group because the process of integration is not just physical. They have to understand how we play, which is not easy."