Walters' current deal runs out next summer and he was the subject of a bid from Norwich last week, understood to be around £1.5million.
It was rejected by Stoke and, after Saturday's 1-1 Barclays Premier League draw with the Canaries at Carrow Road, Potters boss Mark Hughes confirmed he would like to retain the 31-year-old Republic of Ireland international.
Hughes said Norwich's bid was "nowhere near" Stoke's valuation and added: ''Jonathan wants a little bit more in terms of the lengths of a new contract, but we are hopeful we can come to an agreement.
''But if we don't, then we will probably keep him and let his contract run down.''
Since then, Walters - who did not feature against Norwich due to illness but did play and score in Tuesday's Capital One Cup victory at Luton - has had his say on the matter.
"I want to stay
I've been here five years, this is my sixth season and it's the longest I've been at any club," he said, quoted by The Sentinel.
"When you've been here so long you get to know not just the players, even though there's been a huge turnaround, but the whole club and everyone involved.
"I've got a lot of friends here."
Walters joined Stoke in 2010 from Ipswich and has made over 200 appearances for the Staffordshire club in all competitions, scoring 51 goals.
Regarding talks over a new deal, he said: "There's a contract there but (not one for me to consider).
"People behind the scenes know why and I'll leave it with my agents and lawyer
I can't really go too much into it.
"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.
"Of course I'd be disappointed if I had to leave the club.
"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."
Source : PA
Source: PA