Gakpo has been heavily linked with a move away from PSV Eindhoven this summer with several clubs believed to be interested in signing him ahead of the new season.
The Dutchman has been rumoured to be on his way to England where Leeds are amongst the clubs who are keen to get their hands on the winger in the ongoing transfer window.
De Jong, who rejoined PSV Eindhoven this summer from Barcelona, has admitted that he often talks to Gakpo and still remembers the time when he first broke into the team a few years ago.
The forward challenged the winger to stay at PSV Eindhoven and help them win the league next season before considering moving on from the club.
De Jong told Dutch magazine Voetbal International: “I used to talk to him in the past, I also did it for the Dutch national team and I still do it.
“I saw him come in and see him make strides. When he came, the talent was already there.
“I think he can have another very good season, finish it by winning the league and then take a nice step.”
Gakpo has not ruled out staying at PSV Eindhoven this season as he does not want to jeopardise his chances of being in the Netherlands squad for the World Cup in the winter.