The centre-back was one of his side's star performers in their 4-1 win over Real Madrid at the Bernabeu on Tuesday night and has long been on Barca's wanted list, with president Josep Bartomeu confirming the club's interest on Wednesday.
Goal understands that the Dutchman was first scouted by Barca's former technical secretary Robert Fernandez in the 2016-17 season and that they were immediately convinced of his ability to perform at the top level.
Indeed, Barca had already tried to sign the defender in summer 2017 with a view to loaning him back to Ajax - a move that was rejected by the Amsterdam club at the time.
And it is likely they will be stepping up their attempts to sign him once again in the 2019 summer transfer window, but, with six first-team central defenders already on their books, they will have to look at culling their squad as part of the process.
Head coach Ernesto Valverde only wants four central defenders for the 2019-20 season, with Gerard Pique and Clement Lenglet the only two who are guaranteed their places for the new campaign.
Two who will definitely be offloaded when the season comes to an end are former Arsenal defender Thomas Vermaelen and Colombia international Jefferson Murillo, with both set to depart when their contracts expire.
There is uncertainty over the long-term futures of Jean-Clair Todibo and Samuel Umtiti, however.
Todibo was only signed by Valverde in the January transfer window from Toulouse but has yet to make a senior appearance for Barca.
He did play in a friendly defeat to Girona on Wednesday but does not appear close to breaking into the first-team set-up in 2018-19 and was again absent from the squad list for Saturday's Liga meeting with Rayo Vallecano.
France World Cup winner Umtiti, meanwhile, has played even less than Vermaelen this season due to persistent issues with his knee. He suffered the problem a year ago but played through the pain at the World Cup in Russia and thus aggravated the injury.
As a result, the 25-year-old has struggled to find his best form in 2018-19 and, after rejecting surgery, has continued to receive preventative treatment since.
Despite him being likely to face Rayo Vallecano, he has not been a regular in the current season and, what seemed unthinkable a year ago, there is the prospect he could be sold in the summer, potentially depending on the outcome of a move for De Ligt.
The Liga leaders have, of course, already sealed a deal to sign Ajax's 21-year-old midfielder Frenkie de Jong in the summer at a cost of €75 million (£65m/$85m) and, like that move, they will face fierce competition from Europe's elite for De Ligt.
Barca are concerned that, if they do not move soon, they will be beaten to his signature, with the likes of Manchester City and Juventus still retaining an interest in the player. They do, however, hope that the presence of De Jong at Camp Nou will help convince international and club colleague De Ligt to make a similar move.
They had talks with De Ligt’s representatives in spring last year but never actually had any hope of signing him last summer, and were thus willing to wait until this summer.
Like De Jong, they have put in a lot of groundwork, with Pep Guardiola saying they are looking at three to four positions in the summer - centre-back being one of the areas, with De Ligt still high on the list.
Along with Juve, there is also the potential for Bayern Munich and Real Madrid to enter the race, although there has, as yet, been no concrete movement from either side.