The Yellow Canaries ruled out making a move for the Blues defender despite being closely linked with the England international in the Turkish and English press.
The Daily Mail reported that Fenerbahçe were preparing to make a £2.5 million offer for the experienced defender.
The 34-year-old has spent his entire career at Stamford Bridge and has 78 caps for the England national team.
Fenerbahçe has become a popular destination for Premier League players recently.
The Istanbul giants finished last season as runners-up in the domestic league and are coached by Portuguese manager Vitor Pereira.