The 24-year-old, who has three years remaining on his current deal, had a transfer request rejected by the Potters earlier in the summer.
It has been suggested that a host of European clubs are interested in his services, but Coates has claimed that Stoke have not received an official offer thus far.
"Mark Hughes will decide on that situation, but he is our player and is under contract," Coates told The Sentinel.
"There haven't been offers that I am aware of, but we wouldn't stand in his way if Real Madrid or a club of a similar standing came in for him.
"He has said he has designs to play at the highest level. He needs to play well to attract these clubs and I hope he does. He is a good player and the ball is in Mark Hughes's court."
N'Zonzi made 35 league appearances last season.