The Italy international struck a hat-trick in Fiorentina's win against Hellas Verona on Sunday.
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Di Gennaro told Radio FirenzeViola: "March and April are the key months, there are a lot of games today. He is 24 years old, he must always unleash this strength that he has.
"Now he is like a leader, he felt considered by the coach and the environment. In my opinion Kean is stronger than (Dusan) Vlahovic, he has more shots.
"If he doesn't fall back, he can start a new cycle at Fiorentina. And also keep an eye on (Lucas) Beltran's skills. If another striker arrives, he must fit into a very consolidated group and this is not easy. If Fiorentina were to also beat Inter, then we can really think big."