The Citizens are said to have tabled a £4.5m bid for the 18-year-old defensive midfielder, who is now part of the Turkish outfit's first team after impressing at youth level.
Fener president Aziz Yildirim was quick to reject City's approach as he sees Guctekin as a regular this season, telling reporters: "Manchester City have made a €5m offer for him.
"We turned down the offer. We gave assurances that he will play this season; do not be surprised to see him in the starting XI as a number eight."
According to The Sun this has alerted Arsenal and Spurs, with the North London rivals ready to enter the race for the teenager.
Guctekin signed his first professional deal with Fenerbahce last summer.