Kluivert, 19, was this week revealed as one of five finalists for the 2018 European Golden Boy award – partly as a result of his impressive performances to date with the Giallorossi.
And, having notched his first assist for the club on his debut and his first goal in the Champions League last month, the winger has acknowledged that he is relishing his new life in Italy so far.
“I feel good. I’m really very happy,” Kluivert told Sky Sport Italia on Thursday.
“Every day I’m enjoying things more and more, and I can’t wait to see what else the future has in store for me.”
He added: “I’ve definitely found the right place to grow – even my dad told me that the competition for places will help me improve but I will also learn a lot away from football, living alone for example. But above all I can learn from some great players that play alongside me.
“I know I need to improve every day in the areas that the boss demands more from me. Every day I learn something. I can improve defensively, and I’m working on that. I can also get better in attack, too, scoring more goals.”
The Netherlands international revealed how important club captain Daniele De Rossi has been in his impressive transition to life in the Italian capital.
“De Rossi is very important for me,” he said. “Before I even came here he wrote me a message, welcoming me and saying that he was pleased I was coming and could not wait to start working alongside me. That was a huge boost for me.
“He is really an incredible player, both on and off the pitch, and it’s an honour for me to play alongside him. He speaks English very well and so I speak with him a lot. It’s not easy, but I am trying to speak Italian and hope to improve in the next two months.”
Kluivert could make his latest Roma appearance during Saturday’s Serie A trip to face Udinese – before a crucial Champions League meeting with Real Madrid at the Stadio Olimpico on Tuesday.
“It’s an important game, Udinese are a good side but if we play well we can win,” Kluivert said. “It’s an important game for us.”
“I think Roma we can win the group. I aim to score in every game, and obviously against Real Madrid as well. Everyone should be scared of us when we are at home. I am curious to see how it plays out.
Both games could see the youngster sporting a new hairstyle, after he unveiled a dyed-blond look during training earlier this week.
“The first day everyone was laughing, but now I think they like it,” he joked. “I like to change my look sometimes. I dress a certain way and I always like to try new things.”
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