Zaza made his Italy debut in Antonio Conte's first match in charge, a 2-0 friendly win against Netherlands in September.
And the Sassuolo man then netted against Norway in Italy's opening Euro 2016 qualifier.
His partnership with Ciro Immobile has looked exciting and at the moment, the pair are keeping Liverpool forward Mario Balotelli out of the team and squad.
But Zaza does not view Balotelli as a rival and said he would like to get know the controversial striker.
"I don't consider him a danger," Zaza said.
"As I've always said, Mario Balotelli is one of my favourite strikers around.
"I think that everyone knows about his qualities and what he can bring to any squad.
"I think that Mario could be a part of any national team [and] I don't think he would cast a shadow on me.
"I never had the chance to know him personally - I'd cherish such an opportunity, absolutely."
Zaza's next chance to impress for Italy will come in Euro 2016 qualifiers against Azerbaijan and Malta in the next week.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.