Norwich are understood to have made a bid in the region of £1.5m for the Republic of Ireland international, which is thought to have been rejected out of hand by Stoke.
Stoke have made a number of high profile attacking signings this summer including Xerden Shaqiri, Ibrahim Affelay and Joselu, but it is thought that 31-year-old Walters remains part of Mark Hughes’ plans.
Assistant boss Mark Bowen was only too keen to stress the importance of Walters to Stoke earlier this week.
Walters, who has started both of Stoke’s Premier League games so far this season, has two years remaining on his contract with Stoke after joining the club from Ipswich in 2010.
Over the last five years, the former Blackburn trainee has made 216 appearances for The Potters, scoring 50 goals.
Norwich’s reported interest in Walters will no doubt increase the interest ahead of Stoke’s visit to Carrow Road this Saturday.