Sturridge pulled out of the England squad for the 2-1 friendly win over Brazil at Wembley in midweek after picking up a thigh injury against Manchester City last weekend.
Rodgers plans to leave it late before deciding whether the 23-year-old, who has scored four goals in six games since joining from Chelsea at the beginning of January, is fit enough to feature against the Baggies.
He told Liverpool's official website: "Daniel we're just monitoring over the next couple of days.
"It's not overly serious but we just need to assess to see where he's at. We'll see by Sunday."
Rodgers has confirmed one player who will be available for Monday night's encounter is 18-year-old winger Raheem Sterling, who sat out the England Under-21's win over Sweden with a dead leg.
The manager also revealed he has no other fresh fitness concerns after the midweek international games.
"Raheem was on the field this morning so he'll be fine," he added. "Everyone else is fine."
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