Cash-trapped Barcelona are reportedly ready to do a deal with Manchester United to fund their own transfer targets this summer.
New Red Devils boss Erik Ten Hag is keen to reunite with De Jong, whom he managed at Ajax Amsterdam.
De Jong still has four years left on his Barcelona contract but United are hopeful of striking a deal with the Spanish giants.
Former Barcelona striker Kluivert acknowledges that De Jong has not performed to the best of his abilities at the Camp Nou but he is a special player and will ultimately prove useful when allowed to operate in his preferred position.
"I hope that they will keep him," Kluivert told Cadena Ser. "If they sell him it is clear that the club would receive a lot of money, but it is a long season and Frenkie is not just any player. I wouldn't sell him.
"Busquets is there, who has had an impressive year and it is difficult to remove him but Frenkie can play in various positions. For me, the best is the 6, but Busi's there."
Kluivert also waded in on the potential within his former club, who recovered from a stuttering start under Ronald Koeman to finish second in La Liga under Xavi Hernandez last season.
"They are fantastic, I know them very well, they have grown up in the club and they know the values," he said.
"Ansu is a pity, for injuries this year but he scores important goals for the club. If he is at 100 per cent we are going to enjoy him at Barça. Pedri has not grown in the club but he is a player of another level.
"Xavi, he is the ideal, but you have to give him a little time. Entering how he has entered in a difficult situation, he did very well.
"I don't know if they were fair to Koeman, but they are situations that happen, and I don't know everything that happened, I can't comment. I didn't speak to Koeman when he came out."
