The forward has been touted for great things after an exciting start to life in the Eredivisie, where he has scored five times in 17 outings this season.
“The chances of me leaving are slim,” he 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, who is the son of Netherlands great Patrick, played on Sunday as Ajax defeated NAC Breda 3-1 at the Amsterdam ArenA. He created the equaliser for Donny van de Beek as the home side came from behind to win.
Ajax lie second in the Eredivisie, seven points behind leaders PSV.