According to Sport (h/t Naveen Ullal of Sport Witness), the Premier League side are big fans of the Netherlands international and have made the highest offer for the youngster so far.
However, it's suggested a potential stumbling block for City is that De Ligt is managed by agent Mino Raiola, who is said to have a poor relationship with the English champions and their manager, Pep Guardiola.
According to Mundo Deportivo (h/t Sport Witness), Raiola will play a "fundamental role" in determining where the centre-back will end up should he leave the Amsterdam giants in the coming transfer windows.
It's noted that Raiola visited Ciutat Esportiva de Sant Joan Despi recently to hold a meeting with Barcelona sports manager Pep Segura and sporting director Eric Abidal in an attempt to a establish relationship.
Here's how the story was covered in the Catalan newspaper:
In addition to the teams mentioned, Sport (h/t Ullal) also noted Manchester United, Tottenham Hotspur and Juventus have shown an interest in signing the Dutch prodigy, but the Blaugrana are said to be taking "important steps" to sign the player.
The widespread interest in the defender makes sense, as De Ligt has looked at home at the top level since he burst on to the scene for Ajax. Still just 19, he is a regular in the Amsterdam side's starting XI and has captained them too.
Despite his tender years, he has already made major strides in the game:
As an Ajax academy product, De Ligt will have strong links to the team, and as such, any decision regarding his future will need to be taken with consideration.
The teenager has shown already that he has a rich understanding of the game and is technically outstanding.
What will also be key for the elite teams said to be interested in him will be his ability on the ball, per WhoScored.com:
On paper, he is a natural fit for Barcelona or City, teams that play possession-based brands of football. De Ligt has the game and the temperament needed to step up another level.
At Barcelona, he would have to compete with new signing Clement Lenglet, club icon Gerard Pique and Samuel Umtiti. There's also serious competition for defensive places at City between John Stones, Aymeric Laporte, Vincent Kompany and Nicolas Otamendi.