However, Kluivert insists that moving to Old Trafford would not make sense at this stage of his career, despite an encouraging start to life in senior football.
"I have heard the rumours but I haven't spoken to Mourinho. A move to Manchester United wouldn't make sense, for now," the youngster is quoted as saying by The Metro.
Jose Mourinho has known Kluivert since he was young, having previously worked at Barcelona while his father Patrick played for the club.
Kluivert has made 22 appearances for Ajax across all competitions this season, scoring six goals and creating three more.