The 23-year-old withdrew from England's squad to play Brazil this week with a thigh injury.
Sturridge suffered the injury in Liverpool's 2-2 draw with Manchester City on Sunday, a game in which he scored his fourth goal since joining Liverpool from Chelsea last month.
"I got a knock on my quad and I'm going to get a scan on it," he told the club's website. "Hopefully it's not too serious and I'll be okay for next week's game."
Sturridge was injured in the first half at the Etihad Stadium but played on until being replaced in the 89th minute.
He reported for international duty but a decision was made to withdraw after speaking to manager Roy Hodgson.
Liverpool's draw against the champions came after a 2-2 draw at Arsenal and Sturridge is optimistic those results prove the Reds can push for a top-four finish this season.
Sturridge said: "In our last two games we have played against two great clubs and deserved to win both of the games.
"We'll regroup and get ready for our next game against West Bromwich Albion, which is another massive game for us because they are also challenging for the top places.
"We are nine points off the top four so it's not a massive gap to try and recoup so hopefully we'll be able to do that - we believe we can."