Pictures of Denayer in Istanbul caused a social media stir following reports claiming he will be joining the Lions today.
Denayer is expected to watch the Galasaray v Osmanlispor game at the Türk Telekom Arena before holding final talks with the Istanbul giants.
The report claims that Galatasaray have reached an agreement for City over a loan-deal for Denayer.
The Lions have made strengthening their defensive line a priority over the transfer window and have been targeting younger player recently. Galatasaray also signed 20-year-old Real Madrid midfielder Jose Rodriguez over the summer.
Denayer scored six goals 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 season after winning the league title for a record 20th time last season.