Goal understands that the Catalan giants are closing in on securing a deal for the Dutchman, with press reports in Spain stating that they expect the transfer to be announced in the coming days.
De Ligt, 19, captained Ajax to the Eredivisie title, with his side crowned as champions on Wednesday after a 4-1 win over De Graafschap.
Juventus and Manchester City were both also keen on landing De Ligt, although it appears he will sign for Barca, where he would join up with Ajax team-mate Frenkie de Jong, who has already sealed a €75 million (£65m/$85m) move to the Liga champions.
And, after helping the club secure their first league title since 2014, De Ligt was tight-lipped over a potential switch to Spain.
"This is not the time to talk about my future," he told Fox Sports.
"I don't know if I will go with Frenkie de Jong [to Barcelona]. I still have to analyse things and see everything. We'll see what happens.
"I cannot say anything. We'll see at the end of summer. There is nothing yet."
And De Ligt was delighted with the Dutch side's campaign, adding: "It is indescribable. We have been craving this for five years.
"I enjoyed the cup, the competition, the Champions League and especially the team spirit."
Former Manchester United defender and team-mate Daley Blind also hailed De Ligt as an "extraordinary talent" and praised his leadership skills.
"Not only as a captain was he important to us," the defender said following Wednesday's win. "It's also about his personality.
"He is a leading figure in the squad. He can guide the team in hard times.
"But if he wasn't one of the best, others were. I think that's how we complemented each other this season.
"But he's an extraordinary talent, that's obvious."