The 24-year-old has been at the Brazilian club since signing on January 3, and has nine Brazil Serie A goals in 30 appearances - but has just two goals in his past 16 in all competitions.
Corinthians director of football Roberto de Andrade defended the former Inter and AC Milan man's signing, and put the 27-capped international on the market.
"When we bought Pato, it was because it was an opportunity, he is a great player," de Andrade said.
"He is a kid - still very young - we don't regret it. He will make the fans very happy.
"We can negotiate about him, like any player. But in order to have a negotiation, there must be clubs interested in signing him and Pato so far has not asked to leave."
Pato has been linked to both Arsenal and Tottenham, after switching from AC Milan to Corinthians for £12 million.
