The 16-year-old has established a burgeoning reputation as a goalscoring centre-back this term, shining for Hajduk Split continentally and domestically at youth and level.
Vuskovic has broken into the Hajduk first team over the past few weeks, playing the full 90 minutes in each of their last four top-flight games and helping the team keep two clean sheets.
The 2007-born centre-back scored his first senior goal for the club in a quarter-final cup triumph over NK Osijek earlier this month, and he has amassed an eye-catching eight goals in 17 games at Under-19 level from the heart of the backline.
The 6ft 4in teenager also has one goal to show from four matches for Croatia's Under-17s, and clubs across Europe have unsurprisingly been alerted to his breakthrough.
According to The Athletic, Man City have sought to steal a march on their rivals in the race for Vuskovic and have submitted an offer worth a total of €12m (£10.5m).
The report claims that the Premier League champions would pay €10m (£8.8m) upfront, with a further €2m (£1.8m) in performance related add-ons.
Hajduk Split have not made a decision on whether to accept or reject the bid yet, but they recently tied Vuskovic down to a new long-term deal until January 2026 at the start of the month.
Vuskovic's off-field matters are being handled by renowned super agent Pini Zahavi, who also represents the likes of Robert Lewandowski and Christopher Nkunku.
Vuskovic's father and grandfather both played professionally, while his cousin Moreno Vuskovic represents second-tier side NK Kustosija, and his brother Mario Vuskovic is on the books at Hamburg.
Vuskovic is one of two much-coveted Croatian centre-backs who will be the subject of much interest this summer, as the race heats up to sign RB Leipzig's Josko Gvardiol.
The 21-year-old, who is considered one of the top defensive prospects in Europe, has also been tipped to move to Man City, who could part ways with Aymeric Laporte in order to increase their chances of bringing him to the Etihad.
Chelsea failed to prise Gvardiol away from Leipzig last summer, but the centre-back has since revealed his desire to play in the Premier League, and the Blues are expected to go back in during the upcoming window.
Leipzig agreed a new deal with Gvardiol until the summer of 2027 last year, but that deal reportedly includes a £97m release clause that will become active at the end of next season.