The Brazil international has been heavily linked with a 15 million euro move away from San Siro over the past couple of weeks, with the Brazilian club seemingly the most likely destination.
Club chief Duilio Monteiro Alves has thrown his backing behind the potential capture and said it would be a gift to supporters ahead of the new season.
"A lot of people know about his potential on the pitch," he told ESPN Brasil.
"He is an exceptional player. Our medical department and physiotherapists are already following Pato and are going to work with him.
"We hope that in the first week of January we can give him as a gift to Corinthians' fans."
Pato has been with the Rossoneri since 2007 and has made 151 appearances for the club, though much of his time in Italy has been marred by injury.