Potters' boss Tony Pulis is a long-term admirer of 26-year-old Walters and had a £3m bid rejected in 2008.
Pulis has continued to monitor the former Blackburn and Bolton striker who cost Ipswich just £100,000 from Chester in 2007.
Stoke assistant boss Peter Reid was at Portman Road on Sunday to check on Walters in the 3-0 home defeat by Sheffield United.
Ipswich boss Roy Keane said: "There will be plenty of clubs - there are already - who would be keen to take Jon Walters. At Newcastle, aside from his goal, he was outstanding.
"He has been amazing this year, his captaincy has been excellent and he's been a joy to work with.
"But we have a core group of players we have no intention of letting go, my captain being one of them."