The Republic of Ireland international was forced off in the first half of Wednesday's friendly with Greece after suffering a recurrence of a hamstring problem.
Stoke boss Tony Pulis is now waiting for the results of further assessments on Whelan before he knows whether the 28-year-old will be available for the outing at Upton Park.
"Glenn has had a scan on the hamstring, so we'll wait to see the outcome," Pulis said on Stoke's official website.
"He felt the hamstring tighten up a little, so he took no chance in coming off."
Stoke will definitely be without Dean Whitehead due to suspension against West Ham and so fringe-men Wilson Palacios and Maurice Edu could have an chance in London.
"This might be Wilson's opportunity if Glenn is not fit," said Pulis.
"I've sensed a desire over the past month that he wants to prove to people that he can play in the Premier League."