Arnautovic has reportedly handed in a transfer request after becoming disillusioned with life at the Bet365 Stadium, as reported by Sky Sports.
Stoke boss Mark Hughes has since confirmed the situation and told Arnautovic to 'appreciate what he has' at his current employers.
Charlie Adam celebrates with Marko Arnautovic
But now Arnautovic's teammate Charlie Adam has lifted the lid on the main motivation behind the move - as reported by the Evening Standard - and says Stoke will be losing their best player.
"He wants to look after his family," Adam revealed, as reported by the Evening Standard.
"Marko's a massive figure at the club, I'm going to say it from the players' point of view.
He's a wonderful player and he's done a great job for us but something has changed and he's made a decision. He's our best player."
Some supporters have questioned Arnautovic's quality and consistency, feeling he blows too hot and cold.
But Adam plays and trains with the Austrian international day in day out and his analysis that he is Stoke's best player will be music to the ears of Hammers fans, particularly given they have the likes of Xherdan Shaqiri in their squad.
West Ham supporters have watched on with frustration as their Premier League rivals strengthen this summer while Pablo Zabaleta is Bilic's solitary signing so far on a free transfer from Manchester City.
Arnautovic is Stoke's best player according to Adam
Hearts were in mouths this week when the infamous West Ham injury curse seemed to have struck again after Arnautovic was seemingly injured and had to be substituted in Stoke's pre-season friendly against Neuchatel Xamax.
But he was able to walk to the changing rooms and it is not thought to be serious enough to stop a potential move.