The Reds ace, who netted his fourth goal in six games for his new club, would be a big loss to the Reds who are starting to look like Champions League contenders with Sturridge combining well with Luis Suarez up front.
The 23-year-old is expected to pull out of England's friendly with Brazil in midweek and then it will be a case of if he can recover in time to face West Brom, but the fact that the game is not until the Monday will work in the Reds' favour.
Meanwhile, boss Brendan Rodgers says the player is a doubt for Wednesday at the very least.
"He got a knock just before half-time on his thigh," said Rodgers. "He wanted to give it a go in the second half but he will be a doubt for the game on Wednesday.
"It's a shame because he was terrific, a real threat. His hold-up play, pace and combination with Suarez and Downing up front was outstanding.
"He's going to have a chat with our doctors and they will speak with the England set-up. They may want to have a look at him to see how serious it is but at the moment he's obviously struggling."