The 25-year-old was the architect of Brazil's 3-1 friendly victory over Denmark in Hamburg on Saturday, scoring two goals and setting up the third.
Coach Mano Menezes will name his 18-man squad July 6 and Hulk is vying for one of three places allowed for players over the age of 23.
"We have to make the most of our chances when they come along and of course I will be hurt if I'm not called up," Hulk was quoted as saying by Xinhua.
"Because of the goals I rate that performance as my best so far for the national team."
Other over-age players hoping to be selected include AC Milan's Thiago Silva and Real Madrid's Marcelo.
Brazil's next match will be against the US in Washington on Wednesday. It will be followed by games against Mexico and Argentina in early June.
Brazil winger Hulk anxious for Olympic call-up
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