The 24-year-old has handed in a transfer request at the Britannia Stadium as he seeks a switch to 'the highest level'.
A similar approach last summer saw him secure a move away from relegated Blackburn Rovers, with Stoke offering him a route back to the Premier League.
Nzonzi impressed at times in 2012/13, earning him the Potters' Young Player of the Year award.
There is believed to be interest in his services, but he has three years remaining on his contract and Stoke are under no pressure to cash in.
Potters chairman Peter Coates told The Sentinel: "Mark Hughes will decide on that situation, but he is our player and is under contract.
"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' court."