Sturridge, who has been beset by injury problems for more than a year, has only just returned from surgery on his hip but has picked up another knock in training.
Klopp was left with only 20-year-old Belgian Divock Origi, making his first start, as a recognised striker with Christian Benteke and long-term victim Danny Ings out injured.
"We had a bad week with injuries. The best news is it's not a serious thing with Daniel. But in a week like this with two ACLs, we could not risk it," Klopp told reporters.
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"Daniel had a one-on-one situation with Jordon Ibe in training; I didn't see it but after he said he had a little pain in a muscle," he added after the 0-0 Premier League draw.
"We made a diagnosis and screened him to be sure -- we can see a little bit of swelling but nothing really serious. So we have to see. I hope he's ready to play on Thursday," Klopp added referring to the Europa league group match against Rubin Kazan.
"It's not the best situation at this moment, but I like Divock. And young (Jerome) Sinclair was on the bench and was close to coming in.
"Our club works 24 hours to help the players come back. Danny Ings of course needs time; Benteke doesn't need the same time, he’ll be back next week."
(Reporting by Martyn Herman; Editing by Ken Ferris)
