Kluivert, 18, has been linked with a £10 million move to United, as well as Premier League rivals Tottenham Hotspur, but the son of legendary Netherlands striker Patrick Kluivert knows a move away from the Eredivisie giants may be detrimental to his long-term future.
After helping De Joden to the final of the Europa League last season, where they lost to the Red Devils 2-0, the teenager has become a regular fixture in the club's starting XI, scoring five goals and registering three assists in 14 starts.
"The chances of me leaving are slim," the Netherlands youth international told Voetbal Inside. "I haven't spoken to Jose Mourinho myself. I know as much as you do.
"Rumours are always there, but Manchester United has never come up and I don't think it's a logical step. A few more years at Ajax? Who knows, we'll see."
Kluivert is represented by super-agent Mino Raiola, who brokered deals for Paul Pogba, Zlatan Ibrahimovic, Romelu Lukaku and Henrikh Mkhitaryan to United over the past 24 months.