The Sao Paulo club are looking to add to their attacking options and are considering making a loan offer for the 22-year-old, who has been plagued by injuries this season
The Brazilian club are reportedly in the market for a world-class striker after dispensing with the services of Adriano in March following the 30-year-old's failure to impress as a result of fitness and off-the-field problems.
Pato has endured an injury-plagued season, which has seen him make just 18 competitive appearances since the start of the campaign.
It is believed that Corinthians will try to convince Milan to release Pato on loan and believe their high-end medical facilities will help rid the Brazilian striker of his many niggling injuries.
However, the Serie A giants have not given any indication that they are willing to sell the 22-year-old, who joined the club from Internacional in 2007.
Questioned about the club's reported interest in Pato, Corinthians football director Edu Gaspar told Globoesporte: "We are waiting for the end of the Serie A season to see.
"He is a great player, but this is something that Milan must want, too."