The 25-year-old has scored two goals and registered 12 assists in 128 appearances for the Citizens since making the move from FC Ufa in 2016.
Zinchenko was again an important squad player for Pep Guardiola's side during the 2021-22 campaign, featuring on 28 occasions in all competitions, providing five assists in the process.
The Ukraine international only has little over two years left to run on his contract at Etihad Stadium, though, with his long-term future with the Premier League champions unclear.
According to the Daily Mail, Arsenal are keen to explore the possibility of bringing Zinchenko to the club during this summer's transfer window.
The Ukrainian has largely played as a left-back during his time at Man City, but it is alleged that Gunners head coach Mikel Arteta views him more as a midfielder.
Zinchenko, who has won four Premier League titles, one FA Cup and four League Cups during his time in Manchester, is said to have had a close relationship with Arteta during the former's time as assistant manager of the Premier League champions.
Man City are believed to be keen to sign Brighton & Hove Albion's Marc Cucurella during this summer's transfer window, which could potentially push Zinchenko down the pecking order.
The report claims that Guardiola will not stand in the way of any player that wants to leave the Citizens in the upcoming market, with Gabriel Jesus also being strongly linked with an exit.
Arsenal are believed to be the favourites for Jesus, with the Gunners seemingly keen on a double swoop for the Man City duo to boost their squad for the 2022-23 campaign.
Jesus scored 13 times and registered 12 assists in 41 appearances for the Citizens during the 2021-22 campaign, including eight goals and nine assists in 28 Premier League outings.
The Brazilian could find it difficult to secure regular starts next term, though, as Man City have agreed a deal to bring Borussia Dortmund's Erling Braut Haaland to Etihad Stadium.
Jesus's agent confirmed earlier this month that he had held talks with the Gunners over the possibility of joining the club in the upcoming market.
Marcelo Pettinati told Italian journalist Fabrizio Romano: "We had talks with Arsenal about Gabriel Jesus. We like the project - it's a possibility we're discussing. There are six more clubs interested in Gabriel. He's focused on the final games with Man City; we'll see."
The 25-year-old has scored 95 goals and registered 46 assists in 236 appearances for Man City in all competitions, and he only has little over 12 months left to run on his contract in Manchester.