The Austria international, who can also operate as a forward, was on the books of Stoke from 2013 until the summer of 2017.
Walters also left Stoke in the summer transfer window, joining Premier League rivals Burnley for a transfer fee that could reach £3 million, according to BBC Sport.
The 34-year-old Republic of Ireland international striker believes that selling Arnautovic was a good deal for his former club Stoke.
The former Ipswich Town man has suggested that the the ex-Werder Bremen star is inconsistent.
Walters told BBC Sport about Arnautovic: “Marko could turn it on last year, over the last couple of years he turned it on, when he is on it, he is on it.
“But how many games did he do it during the course of the season? Would he do the other side of it was an issue with him. And could he do it consistently?
“For me, it was probably a good deal for Stoke, but then again, it's a step up probably for Marko. He has probably gone and doubled his wages or whatever. He has to step up. Has he done it? You would say he hasn't.
“When he's on it, he's on it, but that seems the type of player that they have got at the club. When things aren't going their way, they won't be digging in, I wouldn’t say.”
West Ham in the Premier League bottom three at the moment, while Burnley are currently as high as seventh in the standings.