Walters has one year left on his contract and has been in negotiations with the Potters over a new deal, but the club have offered him only a one-year extension rather than the extra two years he is looking for.
Stoke have rejected two offers from Norwich for the forward, the second bid worth around £2million, while Tony Pulis is also interested in a reunion at West Brom.
This follows on from the news that the Republic of Ireland player is yet to join up with the squad ahead of their Euro 2016 qualifiers against Gibraltar and Georgia.
Ireland boss O’Neill said: “There may be something happening, although he’s not terribly sure at this minute.
“But while there is the possibility of something happening to him, then I think it’s best that he sees it until the transfer deadline is finished.
“I said to the players beforehand that I will be prepared if somebody has to go at the last minute, either on loan somewhere, that’s fine, or if it’s a proper transfer.”