The Ukraine international has proven to be a useful option for Pep Guardiola, making a total of 68 appearances for City across the last three seasons.
However, with Nathan Ake now able to offer cover at left-back, the 23-year-old has moved down the pecking order at the Etihad Stadium.
According to reports in Spain, City have contacted Barcelona to enquire whether they have any interest in the player.
While the Catalan giants have not dismissed a future approach, any bid is dependent on whether they are able to sell second-choice Junior Firpo.
Zinchenko still has four years remaining on his contract, leaving City in no rush to sell him for a cut-price fee. body check tags ::