The Colorado are expecting potential suitors to up their interest in the 23-year-old striker after his goal-scoring exploits for Brazil at London 2012
The 23-year-old has been in fantastic form for the Selecao in London, scoring four goals in as many games to help his nation reach the semi-final stage.
His coach at Inter, Fernandao, has admitted he believes the player's performances mean the club will face a huge increase in interest for the striker who has previously been linked with Paris Saint-Germain, Tottenham Hotspur and Juventus.
The trainer was also keen to point out the difference between any potential transfer of the striker and that of his former team-mate Oscar, who recently joined Chelsea.
"There will be offers, I have no doubt. In the last four transfer windows there have been offers and the board have worked to keep Damiao," Fernandao said to Radio Gaucha.
"Oscar only left as his release clause was met, we could do nothing about it."
His statement was echoed by the Porto Alegre club's vice-president, Luciano Davi, who believes that every strike Damiao nets will bring about another bid.
"With each goal that he scores, there is a bit of horror. If a proposal comes, Inter will look at it," he said.
Damiao will be hopeful of retaining his starting berth as Brazil take on South Korea in the semi-final of the Olympics on Tuesday, August 7.