Despite Benjamin Mendy's police charge and subsequent club suspension, Zinchenko struggled to become a regular first-team starter under Pep Guardiola last season.
With Joao Cancelo often preferred at left-back, Zinchenko was restricted to just 15 Premier League appearances in 2021-22 - 10 of which came from the first whistle.
Furthermore, with the Premier League champions also in pursuit of Brighton & Hove Albion's Marc Cucurella, Zinchenko has been tipped to end his trophy-laden stint in Manchester.
Arsenal were credited with an interest in Zinchenko earlier in the window, but speculation over a move to the English capital cooled as the Gunners focused on other targets.
However, Arsenal quickly reignited their pursuit of the Ukraine international, and according to transfer expert Fabrizio Romano, a move is now nearing completion.
Zinchenko is understood to have agreed terms on a four-year deal with the Gunners until 2026, and he is keen to reunite with former Man City assistant Mikel Arteta.
Arsenal will reportedly fork out an initial £30m to sign the 25-year-old, which could rise to £32m with performance-related add-ons that are said to be 'achievable'.
Zinchenko is now expected to undergo his medical with Arsenal before an official announcement is made, and he could then link up with Arteta's squad for the remainder of their pre-season tour of the USA.
Man City are already in North America for their own exhibition period, and Zinchenko could therefore say his goodbyes to Guardiola and his teammates before making the short journey to link up with Arsenal.
Zinchenko prepares to leave Man City having registered two goals and 12 assists in 127 games in all tournaments, including five assists from 28 appearances in the 2021-22 campaign.
The former Ufa and Shakhtar Donetsk man won his fourth Premier League title last season, and he has also scooped four EFL Cups, one FA Cup and two Community Shields at the Etihad.
Arteta is understood to have been attracted to Zinchenko's versatility, with the 25-year-old often deployed in the heart of midfield during international matches for Ukraine.
Arsenal have been in the market for engine room additions in the summer window, and Zinchenko would become the club's fifth summer arrival after Marquinhos, Fabio Vieira, Matt Turner and ex-City teammate Gabriel Jesus.
Thursday's clash with Orlando City is expected to come too soon for Zinchenko to make his debut, but the left-back could be available for the weekend's Florida Cup contest with Chelsea.
The Gunners will then return to the UK to face Sevilla before beginning their Premier League season against Crystal Palace on August 5.