The 24-year-old Frenchman, who only joined the Potters from Blackburn last summer, set his sights on a move away from the Britannia Stadium before the departure of manager Tony Pulis.
However, Stoke's young player of the year still has three years remaining on his contract and the club are keen to keep him.
A statement on the club's website read: "Stoke City can confirm the club has rejected a written transfer request from midfielder Steven Nzonzi.
"Contrary to reports in the local media, the French midfielder tabled his request earlier this week before the departure of Tony Pulis from the Britannia Stadium.
"The club intend to make no further comment on this matter."