News of the Canaries’ bid for the Republic of Ireland forward was leaked before the sides met at Carrow Road on Saturday.
Walters missed that game because of illness and Hughes later confirmed an offer for the 31-year-old had been rejected – he is out of contract at the end of the season.
Hughes said: “He knows my feelings – we want him to stay. Norwich did make a bid but it was nowhere near our valuation of what Jon gives us, so that was sent back very, very quickly.”
The Potters manager also said it was “predictable” that news of the bid for the former Ipswich Town forward would be leaked before the game.
“That was a bit of mischief, if I’m honest, that’s probably what it was,” he added.
“It happens – I have probably been guilty of it myself in the past so I’m not going to be holier-than-thou and criticise Norwich for that.
“He wants a bit more in terms of length of contract, that’s fair to say, but we hope we can come to an agreement. If he doesn’t sign, then we will probably just keep him and run his contract down.”