The 19-year-old signed for the Italian giants in June, with Roma paying an initial 17.25m euros (£15.16m).
Kluivert, the son of former Netherlands striker Patrick, signed a five-year deal with the Serie A club and he has impressed during his first seven months in Italy.
He has scored just one goal in 12 league appearances but the youngster is loving the extra pressure in the Italian capital.
"The level is higher here," Kluivert is quoted as saying by ESPN. "That's also why I chose to come here. The level is higher. I expect more of myself now. I want to be better every day. It doesn't matter how old you are.
"I think when you're ready for the next step, you have to go for it. And I felt that I was ready for the next step."