The Dutch club qualified for the Champions League group stages on Tuesday, beating Dynamo Kyiv 3-1 on aggregate.
And De Jong subsequently confirmed that he would be staying in the Netherlands, after attracting interest from the Spanish club.
Indeed, reports suggested that Ernesto Valverde's side were ready to spend big to land the 21-year-old as they look to stiffen their midfield, but De Jong is now hoping that he will be able to play against the Catalan giants instead of for them.
"Maybe someday I'll join Barcelona, but not this season," he told NOS. "I'm staying at Ajax. I think it will be a good year.
"I'd love to play with Ajax against Barcelona. Our squad is good and we deserved to reach the group stage. Now we're about to find out what we're capable of in the Champions League.
"It will be my first time [facing those big opponents], but I hope to draw a group with perspective to march on."
Goal understands that Barca's initial idea was to sign both De Jong and Matthijs De Ligt in the summer of 2019, though they tried to execute that plan early upon hearing of interest in the pair from other European clubs.
Ajax have enjoyed a productive summer, re-signing Daley Blind from Manchester United, and also acquiring Dusan Tadic from the Premier League, luring him to Amsterdam from Southampton. Hassane Bande and Zakaria Labyad have also joined the club, bolstering their quest to reach the Champions League proper.
The club entered the competition at the second qualifying round, beating Sturm Graz, before then defeating Standard Liege and Kyiv.
De Jong has made 46 appearances for Ajax in total, scoring eight goals and providing 11 assists.
The young midfielder has been capped at each Netherlands youth level up to the Under-21s and is set to earn his first full cap having been included in the provisional squad for the September internationals against Peru and France.