The 23-year-old has been linked with a move to England for the past few years, with Spurs reportedly the most eager on securing the Brazilian's signature.
The North Londoners failed with a deadline day bid for the Brazil international, but Damiao is adamant that he wants to see out his current contract.
"[Internacional's] president Giovanni Luigi knows I always wanted to stay at Internacional, regardless of any offers that could come," he told Correio do Povo.
"I certainly thank Tottenham [for their interest], they are a big club in Europe, but my focus is on Inter.
"I hope to help Inter for a long time, I have a long contract and I am very happy and focused."
Damiao has 14 caps for Brazil.