Kluivert has come to prominence this season under Erik ten Hag after impressing with cameo appearances last term.
The 18-year-old has scored seven Eredivisie goals in 24 appearances in 2017-18, helping keep Ajax's slim title hopes alive as they chase leaders PSV.
His exploits in Amsterdam have alerted some of Europe's top clubs, with United said to be at the front of the queue should Ajax wish to cash in on one of their best young talents.
"I'm very proud of him. He's doing very good at Ajax," Patrick Kluivert told Omnisport, speaking courtesy of Hublot.
"He's now a first XI player. If he's playing like this in the long-term, he could be one important player in the future.
"Of course, I prefer that he goes to Barcelona but in football everything can happen.
"He's an adult, he can make his own decisions but he's already said it's a dream for him to play for Barcelona. But you never know in football."
Patrick Kluivert's fondness of Barca also makes him believe Ernesto Valverde's side can win the Champions League this season.
"There are some good teams capable of winning it [the Champions League]," he added.
"It's important to be in the quarter-finals. Barcelona are one of those teams.
"It's hard to say who will win it, but Barcelona are playing very well and winning the important games."