Tottenham, Arsenal and Liverpool have been linked with making move for the Stoke star.
Speaking to Sky Sports, Stoke chief executive Tony Scholes remained non-committal over the future of N’Zonzi, admitting that keeping him at the Britannia Stadium could be out of their hands.
He said: “In terms of Steven, and other members of the squad, we are talking and are in constant touch with the representatives and the players themselves. Steven's a great footballer, and obviously player-of-the-year, and we would dearly love to keep him but we will see.
“We don't want to be losing players of quality like Steven, but that's not always in our hands.”
This gives a boost to a selection of Premier League clubs, who have been linked with making a move for the midfielder this summer.
France Football claimed earlier this week that Arsenal, Liverpool and Spurs are all tracking his availability, knowing that he is heading into the final 12 months of his contract, with Stoke maybe looking to cash in on him.
If no new contract can be agreed this summer, the Potters will look to sell the former French youth international, knowing that they could lose him for free next summer.
Whilst naturally a defensive midfielder, he acted in a box-to-box capacity last term, adding drive and energy to a midfield lacking in physicality. He impressed in the 38 appearances he made, scoring three goals and registering one assist.
Per game, N’Zonzi completed 1.9 tackles, 1.2 clearances and 0.8 interceptions, as well as having a strong attacking output, with 0.9 key passes, 1.2 shots and 1.2 dribbles every game.
He is a vital part of Stoke’s first-team set-up, and whilst his future is in the balance, all the interested Premier League clubs will look to make moves for him.