The Dutchman has refused to discuss his future with the Gunners until the end of the season, which has prompted speculation that the 28-year-old could be nearing the exit door from the Emirates.
Despite the North London side's resurgence in the Premier League, Kluivert believes that the prolific striker is destined for another club.
"He is a player who is a leader in the strikeforce of Arsenal, a leader in the team, but for Robin it is nice to look forward to another club to win prizes," Kluivert told talkSPORT. "That is the most important thing.
"He can't do anything any better with Arsenal. He needs to win big prizes. As a player, you want big prizes and I think if he goes to another club he can achieve that."
The Dutchman is expected to be named the PFA Player of the Year this weekend.