Walters, 31, is out of contract at the end of the season and both manager Mark Hughes and chairman Peter Coates have urged him to sign the new deal.
But Walters, who was on target in Stoke’s Capital One Cup success at Luton Town on Tuesday night, has made it clear that he won’t be signing unless the terms of the deal are changed.
He said: “In my eyes if they valued me it would be there and it’s not there. So talk’s cheap when it comes to things like these and I’ll leave it for the men behind the scenes to sort out.
“There’s a contract there but people behind the scenes know why and I’ll leave it with my agents and lawyer. That’s it. I can’t really go too much into it.“Of course I’d be disappointed if I had to leave. I’ve been here five years and we’ve improved every year and I can give you every stat for those years and I’m probably in the top two for everything.”
Meanwhile, Walters’ Ireland team-mate John O’Shea hinted he will make a move into management when he hangs up his boots.
The Sunderland centre-half has been doing his coaching badges and admits the prospect of management is appealing.
He said: “I would like to give it a go but where do you start at a management level?
“I have almost got my A licence at the minute so it is something I will be prepared for if I want to go that route.”