Zinchenko has been heavily linked with a move away from the Etihad Stadium throughout the summer, but just one week now remains in the European transfer window.
La Liga outfit Real Betis are understood to be leading the race for the 21-year-old's signature, but the Manchester Evening News reports that the Premier League champions are unwilling to sanction a temporary exit.
City are open to permanent offers for the versatile midfielder, though, and would consider either a standard transfer or a loan with an obligation to buy from Betis.
Reports in Spain have mentioned a fee of £10.8m, but City are expected to hold out for a bigger offer than that, having seen £19m bids from Fulham and Wolverhampton Wanderers turned down by the player earlier this summer.
Zinchenko made 14 appearances for City last season and is thought to be willing to fight for his place in the team, although he is down the pecking order in both his preferred midfield role and his makeshift left-back spot.