The 19-year-old winger has revealed he rejected a contract offer from the club and plans to leave in the near future, accusing the decision makers of being motivated by money.
But the Netherlands international went further when he revealed that he found out "at the last minute" that an offer from Tottenham had been rejected.
Ajax confirmed to Dutch newspaper Volkskrant that the Premier League side asked about Kluivert after negotiations for Davinson Sanchez in 2017, saying: "Spurs' proposal was that Kluivert would play in Amsterdam for another two years and that he would then go to Spurs. We did not go further on that, because we wanted to renew Justin's contract."
Kluivert, however, did not appreciate the club's decision and feels it shows that they treat the handling of players' futures "like a game".
"I heard that at the last minute," Kluivert told Volkskrant as he continued his criticism. "That says nothing about Ajax, but about the people in the club. Somewhere they were laughing. You see how the football world works.
"If you get higher up, it looks like a game. They do what they want. I'm getting that feeling again now: they do what they want.
"I had two years contract and thought, 'Do it.' My idea was to stay. But then it turns out different.
"As a youth player, you see none of that. As a boy, everything is still fun. You have a nice game on Saturday. As soon as you get higher up, it is often about everything but football, it's all about peripheral issues."
Kluivert, who has scored 13 goals in 56 appearances for Ajax, is contracted to the Eredivisie side until June 2019.