The Athletic report that City are open to selling him if their valuation of him is met. A deal for the Ukrainian would be Arsenal's second summer raid on the Premier League champions following Gabriel Jesus' switch to north London at the start of July.
Arsenal have been on the lookout for a left-sided defender and were monitoring Ajax's Lisandro Martinez who looks set for a move to Manchester United.
Zinchenko's versatility in defence and midfield could provide the Gunners with much-needed ammunition next season and former City manager Stuart Pearce has no doubts about what he would bring to Mikel Arteta's set-up.
"Zinchenko would be a good signing for anybody," Pearce told talkSPORT.
"They've got [Kieran] Tierney at Arsenal, but he gets a lot of injuries.
"The fact Zinchenko can play in various positions, he can slip into midfield and a more advanced position, as he does for Ukraine."
Former City winger Trevor Sinclair echoed Pearce's comments and while he understands why Arsenal are set to swoop for the 25-year-old, Sinclair hopes Zinchenko continues his adventure with City.
"He came to Man City as a midfielder, Pep Guardiola was the one who transitioned him into the full-back role," he said.
"I like Zinny, I think he's been a great servant for the club and he's shown great courage since what has happened in Ukraine. He's very adaptable and seems a really good guy to have around the changing room.
"It doesn't surprise me [the links to Arsenal]. Arteta worked with him at Man City and he knows the great quality he's got, what a great kid he is and how he's matured.
"I think he can probably also see that he's a player who is a bit frustrated. He's been at Man City for a long time and he doesn't really play the A-games.
"Nuno Tavares has struggled a bit at left-back, he's been a bit hit and miss, so it's understandable why they want back up and someone who can play in that role.
"Plus Arteta might change the formation to give different options to the side.
"Zinchenko is a top player and, really, I hope for Man City's sake that he stays!"
Zinchenko joined City in 2016 and has gone on to win four Premier League titles with the club but could only register 15 Premier League appearances last season.
Should he make the switch to the Emirates Stadium, Zincheko will be in familiar company having played under Arteta during the Spaniard's three years spell as City assistant manager, between 2016 and 2019.