The Gunners suffered a demoralising 2-0 reversal at home to Swansea City last Saturday and followed it up with a 2-1 defeat away to Olympiakos in their midweek Champions League fixture.
A bout of injuries mean that Wenger's side will now have to make do without a number of first-team regulars against the high-flying Baggies at the Emirates Stadium.
"Lukas Podolski and Theo Walcott are out," the Arsenal boss announced. "Bacary Sagna and Laurent Koscielny are not back.
"From Tuesday night in Greece there are no new injuries so we have a selection from the combined squad of Tuesday and Saturday."
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"It is a hamstring," he explained. "It should be short-term."
The 63-year-old is also expecting Andre Santos to return to action in the near future, with the Brazilian not having featured since November's win over Tottenham in the north London derby.
"He will not be ready for Saturday but he is not far away with an abdominal injury," Wenger concluded.