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 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.
|6/4||Leandro Damiao is 6/4 to be the top goalscorer at London 2012 with bet365|
"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 August 7.