The Dutch teenager was being linked with a potential move to Manchester United to improve Jose Mourinho’s options on the wing.
Kluivert scored 10 times in 30 games in Eredivisie last season as the Netherlands international helped Ajax to finish in second place in the table.
The exciting winger came up against Manchester United in their 2-0 loss to the Premier League side in the Europa League final in 2016-17.
Kluivert’s father spent six seasons at FC Barcelona and won the La Liga title in 1998-99 before his move to Newcastle United in 2004.
Justin, who has earned one Netherlands cap so far, completed a £17m move to Serie A giants and Champions League semi-finalists AS Roma.
However, the former Ajax striker hinted that his son Justin wasn’t ready for a move to FC Barcelona or Manchester United.
“He chose Roma,” Kluivert told ESPN FC. “It was a good move.
“I think FC Barcelona or Man United was a step too early for him. In Rome, he can develop as a player. I am happy for him.”
Manchester United signed Brazil international Fred in a £52m deal from Ukrainian Premier League champions Shakhtar Donetsk earlier in the summer transfer window.
The Red Devils have also snapped up Portuguese defender Diogo Dalot in a £17m switch from FC Porto.
Lee Grant completed a surprise move to Manchester United from Stoke City earlier this month.
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