The 22-year-old is beginning to impress some of the biggest clubs in England, with Chelsea and Tottenham Hotspur also said to be keen on the player.
Zabarnyi has started all 12 Premier League matches for Bournemouth at the start of the 2024-25 term, helping the Cherries to stay away from trouble at the foot of the division.
Despite his tender years, the centre-back also possesses considerable international pedigree, having represented Ukraine on 45 occasions since making his debut in October 2020.
After making the high-profile £24m switch from Dynamo Kiev in January 2023, Zabarnyi has featured on 59 occasions for Bournemouth, scoring once.
Man City, Chelsea 'handed boost' in Zabarnyi pursuit
According to Football Insider, Premier League sides such as Manchester City, Chelsea and Tottenham have been given a boost in the race for the services of Zabarnyi.
The report states that Bournemouth are willing to accept big-money offers for the centre-back during the summer transfer window at the end of the campaign.
It is understood that the Cherries would not stand in the way of a transfer for Zabarnyi if the purchasing club could offer Champions League football and significant wages.
With extensive experience in the Premier League and on the international stage already, Man City supposedly view the Ukrainian as an exciting potential arrival.
After signing an extension at the Vitality Stadium in the summer, Zabarnyi's current Bournemouth deal does not expire until 2029, meaning that Andoni Iraola's men can drive a hard bargain for the defender.
Man City need fresh faces
Following the narrow 1-0 win over relegation-threatened Southampton on October 26, Man City have lost five straight matches for the first time under the reign of Pep Guardiola.
The absence of Balon d'Or winner Rodri has often been used as an excuse for the Citizens, however there are signs that the Premier League champions have issues all over the pitch.
Signing a two-year contract extension earlier this month, Guardiola has spoken of attempting to build a new team who can continue the era of success at the Etihad.
At the age of 22, Bournemouth's Zabarnyi has the potential to blossom into a world-class defender on the blue side of Manchester with coaching from the Spaniard.