The Gunners have prioritised a move for Zinchenko after missing out on Ajax defender Lisandro Martinez, and are hopeful of wrapping up a deal for the Ukraine international to continue their summer recruitment drive.
Arsenal technical director Edu is leading talks with City, who could demand as much as £35m for the 25-year-old.
Zinchenko is an attractive option for Arsenal because of his versatility.
He is comfortable playing in midfield or at left-back and is a player Arsenal have been monitoring all summer.
Arsenal have been looking to strengthen at left-back but cooled their interested in Martinez, who looks set to join Manchester United.
Arteta worked with Zinchenko when he was assistant to Pep Guardiola City.
Zinchenko has two years left on his contract but City are willing to sell if their valuation is met as they continue to overhaul their squad.
City have already sold Gabriel Jesus to Arsenal for £45m and Raheem Sterling to Chelsea for £47.5m. Zinchenko made just 15 appearances as City won the Premier League last season.