The Dutch giants are acutely aware that Old Trafford chiefs want to bring the talented 18-year-old to Manchester this summer, with Jose Mourinho having known him since he was a small boy.
Mourinho was a coach at Barcelona when the starlet's father, Patrick, was leading the forward line at the Camp Nou and he established a decent friendship with the family.
The Red Devils are hopeful a fee of around £10m would be enough to persuade Ajax to part with the youngster, who is also believed to have had his head turned by the prospect of playing for them in the Premier League.
Reports in the Netherlands, however, insist Ajax value the Dutch Under-21 starlet at more than double the figure United are considering, factoring in his age and the fact he is already playing at first-team level.
The Manchester giants are determined to find better value in the market during the next couple of years by snapping up younger talent although Ajax are not seemingly about to do them any favors on Kluivert Jnr.