But the Potters were unwilling to sanction his sale without bringing in a replacement and Walters' departure was called off when Stoke's move for Crystal Palace's Mile Jedinak broke down.
The Republic of Ireland international has been in fine form this season scoring in three straight games, including in Stoke's first Premier League win of the season against Bournemouth on Saturday.
"In 99 percent of cases, it's about finding a compromise," Scholes told BBC.
"We hope it'll be sorted on our terms, he hopes on his terms. Players will always want what they believe they're worth and why shouldn't they?
"As players get older, the terms of the contract become important. But, as a club, we have to be careful not to over-extend ourselves.
"We disagree with him on the contract he should have going forward and we have not been able to agree anything yet."
(Reporting by Shravanth Vijayakumar in Bengaluru)
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