Mikel Arteta's side have already signed Gabriel Jesus from the Premier League champions this summer and now look set to make it a double raid on the Citizens with the acquisition of Zinchenko.
According to Italian journalist Fabrizio Romano, the two clubs have reached an agreement over a £30m deal for Zinchenko, who is now discussing personal terms with the North London outfit.
The Ukrainian made 28 appearances for the Citizens during the 2021-22 campaign, contributing five assists, but he only featured on 15 occasions in the Premier League.
Zinchenko only started 10 league matches in 2021-22, meanwhile, with the left-back regarded as a squad player at the Etihad Stadium rather than than an important first-team regular.
Arsenal boss Arteta worked closely with Zinchenko during his time as assistant manager of Man City, and the Spaniard is said to be the driving force behind the deal.
A recent report claimed that the Ukrainian is desperate to play more regularly next season and knows that he has to leave the English champions for that to be the case.
The four-time Premier League title winner has scored twice and registered 12 assists in 128 appearances for Man City since making the move from FC Ufa in 2016.
Zinchenko has largely operated as a left-back for the Citizens but operates as a midfielder for his country, and it is believed that Arteta views him as a midfielder rather than a defender.
The player has won four Premier League titles, one FA Cup and four League Cups during his time in Manchester but is now seemingly set to follow Jesus to Arsenal.
Arsenal have already signed four new players during this summer's transfer window, bringing in Marquinhos, Matt Turner, Fabio Vieira and Gabriel Jesus.
The Gunners are also attempting to sign Bukayo Saka to a new contract, with Arteta recently claiming that an agreement with the England international was close.
Arsenal opened their preparations for the 2022-23 campaign with a 5-3 victory over Nurnberg on July 8 before recording a 2-0 win over Everton on Saturday night.
The capital giants are next in action against Orlando City on July 20, while they will also take on Chelsea and Sevilla before opening their Premier League campaign against Crystal Palace on August 5.