The Catalan giants have already sealed a deal to take the Dutch club's exciting 21-year-old midfielder Frenkie de Jong to Camp Nou in the summer at a cost of €75 million (£65m/$85m).
And Barca president Josep Maria Bartomeu has confirmed interest in De Jong's Ajax team-mate De Ligt, 19, as well.
"Where there is such talent away from Barcelona, we're always looking at them.
"It's a topic that will be discussed in our sports planning which begins in March, with De Jong we felt we had to move quickly because there were many clubs that wanted him."
Both of the young Dutchmen starred in Ajax's stunning 4-1 Champions League win over Real Madrid at the Santiago Bernabeu on Tuesday night.
But De Ligt's abilities were already well known to the top clubs of Europe with Juventus and Manchester City also understood to be interested.
Ajax's former Barca back-up goalkeeper Andre Onana said recently that De Ligt wants to join De Jong at Barca, commenting: "De Ligt would also like to go, I talked to him several times and with both of them."
The teenage centre-back emerged during the 2016/17 season, helping Ajax to the Europa League final.
He has also showed a maturity beyond his years alongside Virgil van Dijk in the Dutch national team.
Ajax sporting director Marc Overmars knows his qualities well.
He told Spanish outlet AS: “For me, De Ligt can play easily for any of the six best teams in the world.
“Right now, he has the power, the mentality. He has the heart.
“If I worked at another club, I would like to sign him immediately."