N'Zonzi has one year left on his current contract and could leave the club this summer.
N'Zonzi, who has one year remaining on his current contract, will not sign an extension at the Britannia Stadium and reportedly wants a move away from the Potteries.
It would represent a huge blow to Hughes and his side as the fine form of the Frenchman helped them to a comfortable finish in the top half of the Premier League - with N'Zonzi picking up the club's Player of the Year prize.
The report also says it's not the first time the Stoke boss has done such a thing, and has managed to persuade N'Zonzi to stay put during each of the last two seasons.
If he doesn't manage it this time, then that will be a blow for Potters going forward. The presence he offers in the middle of the park is quite intimidating - though some can be misled by his stature given the quality he has with the ball at his feet.
He also has the ability to find the net regularly from range. One only needs to look at goals against Liverpool and Manchester United over the course of last season to see that he has that attribute in his locker.
Losing the Frenchman could be painful for Stoke but it is certain that they won't want to lose him on a free transfer next year. It seems that N'Zonzi will either have to sign a new contract or be sold. Mark Hughes hopes it will be the former.