The report claims that Galatasaray have reached an agreement for City over a loan-deal for Denayer.
City want a €1.5 million sign-on fee while the Istanbul giants want to include a buyout clause option as part of the deal.
Denayer is expected to arrive in Turkey today and attend the Galatasaray – Osmanlispor game at the Türk Telekom Arena this evening.
The Lions take on newly promoted Osmanlıspor in their first home game of the season.
The 20-year-old defender netted six times and provided two assists in 44 appearances for Celtic in all competitions last season.
The Istanbul giants booked a place in the Champions League group stages for the fourth consecutive season after lifting the 2014-15 title for a record 20th time.
Galatasaray won the league and cup double, earning the right to become the first club to wear the fourth star on their crest.