The former AC Milan forward has been with the club since January, but recent reports have suggested he could be on the move.
However, De Andrade says that while Pato will not leave for another Brazilian club, a move elsewhere is possible.
"Considering his value, I think it's hard that he moves to another Brazilian club," Radio Bandeirantes quotes De Andrade as saying.
"If those two clubs (Arsenal and Tottenham) are interested in Pato, we don't rule out selling him in the winter transfer market."
Pato joined Corinthians for £12.2m.