Matri left Juventus for Milan last month.
I do dream of the national side," admitted the 29-year-old. "And I want to give it a go. Doing well for my club will only increase my chances of convincing boss Cesare Prandelli.
"I want to be an important player and I want to assume my responsibilities in this Milan side, a club where I was born and grew up in footballing terms.
"I always work hard to demonstrate my qualities."
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