The 25-year-old is allegedly close to completing a £35m move to the Emirates Stadium following positive talks held between both clubs.
It is thought that Gunners boss and former City assistant coach Mikel Arteta regards Zinchenko as their primary left-back target, after missing out on Manchester United-bound Lisandro Martinez and Brentford's Aaron Hickey.
Nevertheless, Pep Guardiola has included the versatile Ukraine international in his travelling squad to the States, with the Premier League champions scheduled to face Club America and Bayern Munich.
Summer signings Erling Braut Haaland, Kalvin Phillips and Stefan Ortega have also been included, along with January recruit Julian Alvarez.
Haaland officially joined the Citizens on July 1 after they activated the £51m release clause in his Borussia Dortmund contract, while Phillips and Ortega have joined from Leeds United and Arminia Bielefeld respectively, the former of whom arriving for an initial fee of £42m.
While City's four new signings are notable additions for Guardiola's squad, there are also four standout absentees in the form of Phil Foden, John Stones, Aymeric Laporte and Ilkay Gundogan.
All four players will not be joining the rest of the first-team squad in the USA and the Citizens are yet to provide an explanation for their absence.
A previous report has claimed that Foden, Stones and Gundogan will instead join up with City's Under-23s squad and travel to a European destination to continue their preparations for the new season, with Laporte now seemingly set to do the same.
There is also no place for backup goalkeeper Zack Steffen, who is allegedly on his way to Championship outfit Middlesbrough on a season-long loan deal.
Elsewhere, Riyad Mahrez and Rodri will be in buoyant mood as both players put pen to paper on new contracts at the club.
Rodri, 26, has signed a new three-year extension until the summer of 2027, while Mahrez, 31, has penned a two-year extension, keeping the winger at the club until June 2025.
Portuguese playmaker Bernardo Silva has also been named in Guardiola's pre-season squad, despite reported interest from Barcelona, who are understood to have identified the 27-year-old as a potential replacement for Manchester United target Frenkie De Jong.
Former Chelsea target Nathan Ake, last summer's £100m man Jack Grealish and the 2021-22 Premier League Player of the Season Kevin De Bruyne are also also among the names included in City's squad.
Manchester City's 26-man squad in full:
Kyle Walker, Ruben Dias, Kalvin Phillips, Nathan Ake, Erling Braut Haaland, Jack Grealish, Oleksandr Zinchenko, Rodri, Kevin De Bruyne, Stefan Ortega, Julian Alvarez, Bernardo Silva, Riyad Mahrez, Joao Cancelo, Ederson, Scott Carson, Liam Delap, Kayky, Luke Mbete, Cole Palmer, James McAtee, Josh Wilson-Esbrand, Oscar Bobb, Rico Lewis, Finley Burns, Ben Knight