The 23-year-old has been linked with Tottenham Hotspur, Inter Milan and Manchester United throughout the summer, and although he did not reveal which club made him an offer, he reiterated his desire to continue playing in Brazil.
Damiao told BandSports: "The value of the offer was very good for me and for Internacional.
"But it didn't happen. I think Giovanni Luigi is a great president and he knows what he's doing.
"I'm very happy to be playing in Brazil. I'll certainly leave at some point for sure, but not today."
Damiao finished as top scorer in the Olympics football tournament last month.