The Hammers have already launched an official bid for the Austrian and Arnautovic has told his current club that he wants to leave for the London Stadium, but Stoke are refusing to budge.
Arnautovic was absent as the Potters kicked off their pre-season with a 4-2 defeat to Monaco on Saturday but the forward did make the trip to Martigny for the game.
According to our colleagues at the Stoke Sentinel, the Potters expect Arnautovic to return to full training with the rest of the squad next week.
The 28-year-old has been undertaking light fitness training following a knee injury.
Stoke boss Mark Hughes explained: “Marko has just got an issue with the inside ligament of his knee. He should be fine next week.”
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