"It seems that maybe Jon could take the option of a move to Burnley," Hughes was quoted as saying by the Sentinel.
"I haven't had the opportunity to speak to him about it. I think it's something that maybe he wants to make happen, but irrespective of that, if it falls through we would be more than happy because Jon coming back to the club would be fine."
Media reports claimed Burnley would offer Walters a two-year deal with the option of a one-year extension at Turf Moor and Hughes felt Stoke were unable to match the length of contract.
"Maybe at this point of his career Jon feels that he needs a bit more security in terms of length of contract which maybe we weren't prepared to match what he's got on the table," Hughes added.
"If he does go, we will look back on his time here with fond memories. He's been a huge part of the success of the club in the Premier League and his contribution will never be underestimated."
Walters made 23 league appearances last season as Stoke finished 13th in the league.
(Reporting by Aditi Prakash in Bengaluru; editing by Amlan Chakraborty)
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