The Italy striker has had an inconsistent first full season in Serie A.
After victory over Cagliari, Zangrillo said: "The mere fact that he is an Argentine native who has attracted the attention of the national team coaches should say a lot about his qualities.
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"He comes from two difficult seasons, but he is a complete centre forward and it is nice that the national team can count on young people like him and (Gianluca) Scamacca.
"I'm rooting for Mateo in blue and I know he won't disappoint me."