The report claims that Galatasaray have agreed terms with City and that Denayer will arrive in Istanbul tomorrow with his agent, father and uncle.
The Belgium international will enter final talks with Galatasaray on Tuesday.
Denayer scored six goals and provided two assists in 44 appearances for Scottish giants Celtic in all competitions last season.
Sky Sports report that Marseille are also on the verge of signing the youngster.
The Istanbul giants would be able to offer Denayer Champions League football after winning the league title for a record 20th time.
Galatasaray booked a place in the Champions League group stages for the fourth consecutive season after lifting the 2014-15 title.
The Lions have been targeting younger players in the transfer market recently in contrast to previous seasons.
Galatasaray signed 20-year-old Jose Rodriguez from Real Madrid last month and Sporting Lisbon wonder-kid Bruma and young Brazilian full-back Alex Telles recently.