The 19-year-old has generated plenty of interest since bursting onto the scene in Amsterdam - much like his dad did 24 years ago.
It has been suggested that Kluivert Jr will see his career follow a similar path to an illustrious family member, with a spell at Camp Nou considered to be part of his sporting destiny.
Various reports claim that Barca would be willing to make that dream a reality in the not too distant future, but Patrick Kluivert believes it is too soon for his son to be making such a move .
A man who won the 1999 Liga title during a six-spell spell in Catalunya told Ole : “The truth is that now is not the time.
“He is just in his second year in the Netherlands and moving to a club of the magnitude of Barca should not be the first choice.
“For now, go step by step, calmly and calmly, but as a father I will support him in anything he decides.”
While Barcelona may be keen, and Tottenham held talks while discussing a move for Davinson Sanchez in 2017 , it is Serie A side Roma who are reported to be leading the chase at present.
The ex-Milan frontman said: “I try, I tell him, he is 19 years old and thinks he can play with [Lionel] Messi, Luis Suarez, [Sergio] Busquets, [Philippe] Coutinho ... But he has to do more yards.
“When a team sits down to negotiate in earnest, they will have to explain the project, what they want from him, and then it will be my son who decides if he accepts it.”
Justin Kluivert made his Ajax debut in January 2017, netting two goals before the end of that campaign before going on to cement himself as a first-team regular in 2017-18.
In the campaign just gone, the teenage forward delivered 10 goals and five assists in his Eredivisie outings, while a senior international debut for the Netherlands was made against Portugal in March.