Gazzetta dello Sport claims Corinthians have met the €15m (£12.3m) asking price for the 23-year-old, who cost Milan €22m (£18m) in 2007.
Milan vice-president Adriano Galliani said the deal was close and more talks were scheduled.
He said: "The meeting went very well. But the negotiations are still not complete. We’ll meet again in Sao Paulo at the end of the year."
Pato has been plagued by injury, playing just 25 games in the last season-and-a-half.
He has scored 63 goals for the Rossoneri, but has not found the net in Serie A this season.
Pato's fellow Brazilian Robinho is also expected to leave the club in January, with Santos and Atletico Mineiro the most likely buyers.