According to Sam Wallace of the Daily Telegraph, the Premier League champions have been impressed by the development of the 18-year-old, and technical director Txiki Bergiristain paid a visit to Amsterdam on Wednesday to hold discussions with scouts from the Netherlands.
"De Ligt was due to play for Ajax in their Eredivisie game against VVV Venlo on Thursday night although there was no confirmation that Bergiristain would attend the game in person," the report said. "He was there with Gary Worthington, the club's assistant head of player recruitment, for meetings with chief Dutch scout Kelvin De Lang about the club's plans for the summer."
According to Wallace, there are a number of big-name clubs looking at De Ligt, who has already shone at the highest level despite his tender years. Ajax would demand a fee of around £50 million before agreeing to cash in on their defensive starlet.
It's suggested that despite spending a club-record £58 million in the January window to sign Aymeric Laporte from Athletic Bilbao, City do want to add another central defender to their ranks.
The club have invested heavily in recent years to ensure they are secure at the back:
De Ligt would be another costly acquisition, although there's no doubt the youngster is someone with immense potential.
He was a key man last season as Ajax made their way to the UEFA Europa League final. While they lost that match, De Ligt impressed and has continued growing this season; he's taken on more responsibility at the base of the team following the departure of Davinson Sanchez.
For a player so young, his strong mentality has already shone through many times on the field. Dutch football writer Sjors van Veen picked up on the following moment after PSV Eindhoven beat Ajax to secure the Dutch title:
Sjors van Veen @SjorsvanVeen
Matthijs de Ligt unreal mentality for an 18-year-old. Teammate David Neres went straight back to the dressing room after PSV - Ajax (3-0), but De Ligt made a 30-meter sprint towards the Brazilian to get him back to thank the away fans. That's being a true leader. https://t.co/XQeReO04h0
His natural defensive instincts are sharp, meaning the youngster is regularly in the right position to snuff out danger when the opposition venture forward.
The Netherlands international is also extremely comfortable in possession, per WhoScored.com:
After watching Sanchez move on to Tottenham Hotspur last summer and excel in the Premier League, De Ligt will be thinking he can do the same. It appears as though he and Ajax won't be short of offers at the end of the season either.
Even so, he's still young, especially for a centre-back and if he was to move to City he'd face huge competition for a starting berth from Laporte, John Stones, Vincent Kompany and Nicolas Otamendi. Another season at Ajax would potentially be the most sensible step at this juncture.