The Canaries made an initial £1.5m offer for Walters last week and it was also turned down.
Potters boss Mark Hughes remains optimistic Stoke could reach agreement with Walters over a new contract.
The player, currently on a deal that runs out next summer, was this week quoted as saying he wanted to stay with the Staffordshire outfit but felt they were yet to show they truly valued him in recent contract negotiations.
Reports suggest the main sticking point is the duration of extension being offered to Republic of Ireland international Walters, who turns 32 next month.
And when asked about the contract situation on Friday, Hughes said ahead of Saturday’s home Barclays Premier League clash with West Brom: “Jon knows our feeling and my feeling – I’d like him to stay.
“He has his view in terms of the negotiations. We haven’t closed the door and we still think we will be able to get somewhere with it, but it has not been concluded yet.”
Asked if he was disappointed Walters had aired his view, Hughes said: “No – I think they are honest comments.
“Maybe it is borne out of a little bit of frustration. But I have told him my thoughts about what he offers us and the value he gives to the squad.
“Jon is looking for security and a little bit longer maybe than the club feels they can give him.
“But hopefully there is some common ground we can discuss and move it forward.”