Barcelona want to land De Jong now and know a £44.2m deal will be accepted by Ajax.
Dutch giants are happy to sell after signing Daley Blind from Manchester United this week.
But the Amsterdam club want to keep De Jong for 12 more months.
That is the plea issued from director Marc Overmars, who has asked his former club to stay away from De Jong for now.
“Let them [any interested clubs] come back next year,” he said.
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“Let the players play 40 games with Ajax this year.
“They’ll not be allowed to leave, even for crazy amounts.”
De Jong himself has confirmed Barcelona’s interest, telling Ditch TV station AT5 last week: “Yes, you heard that right.”
When pushed on the transfer reports, he added: “That’s what you have to ask Marc Overmars.
“I can not promise (I will stay), of course.
“But as it stands now, I think I will stay with Ajax this season.”
De Jong, 21, is deemed one of the brightest young talents in Holland right now.
The midfielder can also play in defence – two positions Blind himself can cover.
It was thought Blind’s £14.1m arrival from United was set to trigger De Jong’s departure.
Indeed, Barcelona could still move for the player this summer as manager Ernesto Valverde continues to strengthen his squad.
Barca have already spent £60m on new signings and supposedly have their eyes on Chelsea duo Willian and Eden Hazard.
However, replacements for Andres Iniesta and Javier Mascherano appear the more urgent issues right now.