The 19-year-old has been in fine form for Ajax this season, with the striker netting 10 goals in 30 league games.
Kluivert, son of former Barcelona star Patrick, has been locked in contract talks with the Eredivisie side.
However, negotiations have broken down, with Kluivert demanding to be the highest-paid player at the club.
The attacker, who likes to play on the wing, is demanding £1.3m-a-year to stay at Ajax.
Kluivert also wants a large proportion of any transfer fee to be split between him and his agent, Mino Raiola.
And according to The Guardian, Kluivert could be heading to Old Trafford this summer, with Jose Mourinho a huge admirer of the highly-rated youngster.
They also say Kluivert favours a move to United should he leave Ajax.
Ajax’s policy is to pay players no more than £883,000-per-year (€1m -per-year), which has led to Kluivert demanding a bumper sign-on fee to stay with the Dutch side.
United are back in action tomorrow, with Mourinho’s men hosting Watford on the final day of the Premier League season (3pm kick-off).
The Red Devils have already secured second place behind Manchester City, with Mourinho expected to rest numerous stars against the Hornets.
