The Gunners have reignited their interest in the Ukraine international after conceding defeat in two of their previous defensive targets in Aaron Hickey and Lisandro Martinez.
Brentford ultimately won the race to sign Hickey from Bologna, while Manchester United are understood to be on the brink of signing Martinez from Ajax.
As a result, Arsenal elected to test Man City's resolve over Zinchenko, who was strongly linked with a move to the Emirates earlier this summer before the Gunners focused on other areas of the pitch.
However, with City still plotting a move for Brighton & Hove Albion's Marc Cucurella, Zinchenko will be allowed to leave for the right price in the coming weeks.
According to the Daily Mail, Arsenal are now expected to wrap up a £35m deal for the 25-year-old after talks progressed positively between the two parties.
The report adds that Zinchenko was initially reluctant to leave the Etihad, but the left-back is now open to the idea of a switch to North London in order to increase his game time.
Arsenal and City are yet to agree a fee for Zinchenko, but there is hope that the clubs can find common ground on the financial side of things in the coming days.
Gunners boss Mikel Arteta previously worked with Zinchenko during his time as Guardiola's assistant and is believed to maintain a strong relationship with the player, and he is also attracted to the Ukrainian's versatility.
Zinchenko primarily features as a left-back for Man City but will often start in the heart of midfield for Ukraine, and Arteta wants improvements in both areas for the 2022-23 season.
Zinchenko only cost Man City £1.8m to sign from Ufa in 2016, and the defender has since won four Premier League titles, one FA Cup, four EFL Cups and two Community Shields in sky blue.
The former Shakhtar Donetsk youngster has two goals and 12 assists to boast from 127 games for the English champions, but he only started 10 Premier League matches last season.
City have already allowed Gabriel Jesus to join Arsenal in a £45m deal this summer, as well as sanctioning Raheem Sterling's £47.5m exit to Chelsea earlier this month.
With Zinchenko edging closer to an exit, the Citizens are now apparently set to keep hold of Nathan Ake, who was linked with a return to Stamford Bridge.
Should Zinchenko complete his proposed move to Arsenal, the 25-year-old would become the Gunners' fifth arrival of the summer window after Jesus, Matt Turner, Fabio Vieira and Marquinhos.