Denayer is expected to hold final talks before joining the Lions on loan with a future buyout clause.
City reportedly want €1.5 million from Galatasaray for the young defender according to Hurriyet.
Galatasaray ended up losing the game 2-1 at home against newly promoted Osmanlispor and dropped into 13th place with just 1 point after two games.
The Lions travel to Konya next to take on Konyaspor. Denayer would be permitted to play next week if he passes his medical and if Galatasaray register him by the end of the week.
The 20-year-old defender netted six times and provided two assists in 44 appearances for Celtic in all competitions last season.
Galatasaray will compete in the Champions League group stages for the fourth consecutive year this season.