The Dutch legend has impressed since taking charge at De Kuip, guiding them to second last term and he was handed a long-term deal in the summer.
However, Koeman's name has been strongly linked with City and reports claim that the Premier League club's sporting director Txiki Begiristain - who knows him from their time together at Barcelona - is a confirmed fan.
Koeman admits that it is natural for managers, like players, to be linked with big moves but he knows nothing about City.
"Players who develop into internationals are in the spotlight, and it is logical that people look at trainers also," he told Voetbal International.
"But I have nothing else to say, because I simply do not know about [City's] reported interest."
Koeman took the helm at Feyenoord in 2011 after stints in charge of Vitesse Arnhem, AZ Alkmaar, Ajax, PSV Eindhoven, Benfica and Valencia.