The Premier League winners are now on a preseason tour in the United States alongside the midfielder, who has appeared in several games at left-back for the Blues.
The 25-year-old international from Ukraine is anticipated to finalize the transfer by taking a flight back to England soon.
One of Pep Guardiola’s first hires as City coach in 2016 was Zinchenko.
After making 128 appearances in all competitions, he won four league crowns, an FA Cup, and four League Cups.
After striker Gabriel Jesus’ £45 million transfer to the Emirates earlier this month, Zinchenko would be the second player to leave City for the Emirates this summer.