Wolves have lodged a £16million bid for the Ukrainian international who can play along the left flank or in midfield.
Fulham and Newcastle are also said to be interested in the 21-year-old.
Zinchenko yesterday spoke publicly for the first time since Wolves' bid and didn't rule out a move away from the club.
"At this moment I play for Manchester City and I’m so happy to be part of this team," he said. "You never know what will happen in the future but we’ll see."
Zinchenko is currently in America on City's pre-season tour.
First-choice left back Benjamin Mendy is joining up with the squad despite only having just won the World Cup with France, but Fabian Delph isn't involved after his exploits with England.
Mendy is still getting back to full fitness after suffering a cruciate knee ligament injury last season, so Zinchenko is needed in the squad.
However it's believed that City are still willing to sell Zinchenko when their pre-season campaign draws to a close.
Pep Guardiola's team are chasing a midfielder to replace Yaya Toure and Guardiola yesterday referenced Zinchenko as an option to play thre.
"We will decide until the last day," he said referring to the August 9 transfer deadline day.
"We have Fernandinho and Ilkay Gundogan who can play in this position, and Aleks (Zinchenko) can also play there.
"There is also Fabian Delph, and we have one or two young guys."
Wolves have signed goalkeeper Rui Patricio and striker Raul Jimenez so far this summer while activating permanent deals for last season's loan stars Diogo Jota, Willy Boly, Ruben Vinagre and Leo Bonatini.
It's believed Wolves are close to making a couple more additions with central midfield the clear priority.
Romain Saiss played in central defence during Thursday's 1-1 friendly draw with Ajax and Nuno Espirito Santo is considering making that switch a permanent one, leaving Ruben Neves as Wolves' sole senior central midfielder. Morgan Gibbs-White has played there in pre-season and while the youngster's potential is substantial he has still only started three league games in his burgeoning career.