Kluivert has been frequently linked with a number of clubs in Europe - including Manchester United, Barcelona and Roma - while the youngster has previously suggested that his current club tried to sell him to Tottenham Hotspur without his knowledge.
The 19-year-old has indicated that he does not plan on penning another contract with the Dutch giants, but may choose to continue his development in the Eredivisie until next summer.
Kluivert told FOX Sports: "There are exciting moments coming for me. Let's see what they're going to be.
"In the end, it's my decision. I'm not a 100% convinced yet. I have to think things through. To stay at Ajax is definitely an option. It certainly is."
Kluivert contributed 10 goals and five assists in 30 league appearances during the most recent campaign.