The midfielder, just 19, joined the Nerazzurri in January for an initial 11m from Croatian outfit Dinamo Zagreb.
"He's coming along well," Kuzmanovic, who himself joined the club at the start of the year from Stuttgart, told Mediaset.
"He's already picked up a bit of Italian and I'm very happy for him. I think he's got a great career ahead of him.
"My future? I'm staying put and glad to do so. I'm happy to be here. We've been through some difficult moments and we expected to do better, to get into Europe, but we'll improve."