The Galatasaray director revealed that an agreement is not in place as of yet but that talks are promising.
“Nothing has been finalised yet but talks have been promising,” Nazifoglu was quoted as saying by Turkish-football.com.
The Lions want Denayer on a one-year loan after signing the Belgium intentional last season on a temporary move.
The 21-year-old defender established himself as a first team favourite at the Istanbul giants, providing an assist in the Turkish Cup final victory over Fenerbahce.
Denayer has fallen down the pecking order at City and was not included in the match day squad against Sunderland in the opening Premier League game of the season.
The Sun report that if City were to sell Denayer it would cost clubs interested £12 million.
The report claims that Arsenal boss Arsene Wenger has his eye on Denayer as a solution for his defensive crisis – Mertesacker, Gabriel and Koscielny are all currently out.
The Gunners shipped in four goals against Liverpool at the Emirates in their opening Premier League game of the season during their 4-3 defeat.