The Brazilian-born striker is yet to play international football, despite his steady form in the Serie A over the past couple of seasons.
Amauri said he could join Italy if Dunga did not select him in the near future, but the latter implied that he needs the 28-year-old in his side.
"I’m ready to call up Amauri as long as he does not demand a (regular) starting place," the Brazil boss told Gazzetta dello Sport.
"It would be better for him if he enters on tip-toes. Everyone wants Amauri in Brazil but if the lad gets his first match wrong, he’d be destroyed the day after."
Dunga reiterated his rejection to the notion that Amauri demands a regular place, which was suggested by the striker's agent recently.
"Not even Pele demanded a starting place in the Selecao. Amauri should ask Kaka and Ronaldinho, two Ballon d’Or winners, if they have ever demanded a starting place."
Amauri is currently awaiting an Italian passport, after which he could make a decision regarding his international career.