The Sao Paulo-based club have officially pulled out of the race for the young striker after he was named in the Selecao's squad for the Olympic Games in London
The Copa Libertadores winners have long been associated with the 22-year-old attacker as they look to add to their offensive options after releasing Adriano in March.
Corinthians had hoped that Pato would be interested in a return to his homeland in a bid to ensure his place in Brazil's squad for the 2014 World Cup after a season in which he was plagued by injuries.
But Pato's inclusion in the Selecao's 18-man party for the Olympic Games has forced the club to throw in the towel, as the tournament will provide the striker with the opportunity to prove his worth to coach Mano Menezes.
"There is no way for that this deal can happen anymore," Roberto de Andrade is quoted by Globoesporte as saying.
"If he had not been included in the Olympic squad, there would be a chance."
Pato, who cost Milan €22 million in 2007, made just 18 competitive appearances last season, scoring four goals in the process.