Although Walters will be available for Ipswichâ€™s opening Championship fixture at Middlesbrough on Saturday, Keane agreed there was a good chance the transfer would be completed before the transfer window closes at the end of August.
Asked if he had been in discussion with Stoke and whether Walters was likely to leave, Keane said: "Iâ€™ve had loads, all summer and, yes, itâ€™s likely.
"At this moment in time they have not made an offer that the owner feels is acceptable â€“ and weâ€™re delighted with that.
"I think he will be with us for Saturday and if anything itâ€™s going to be in the next week or two.
"Obviously, the Premiership doesnâ€™t start for another week or so and thereâ€™s usually fun and games with negotiations as you would expect, particularly with certain clubs and particularly with certain managers.
"I'd expect this one to drag on a little bit longer. Jonâ€™s aware of it and itâ€™s very hard to stop a player when he has the opportunity to play in the Premiership."