The England international was left out of the Reds squad as Klopp’s first game in charge of the Merseyside outfit ended all square at White Hart Lane.
Sturridge has been struggling with injuries in recent months and managed just seven Premier League starts for the Reds last season.
However, Klopp played down fears surrounding Sturridge’s problem and hinted that he could be ready for Liverpool’s Europa League clash with Rubin Kazan on Thursday night.
Klopp told his post-match news conference at White Hart Lane on Saturday: “We had a bad week with injuries and the best news is that it is not serious with Daniel.
“He had a one-on-one situation with Jordon Ibe and afterwards had pain in the muscle stabilising the knee.
“We screened him to be sure and could see a little bit of swelling but it’s nothing really serious. I hope he will be ready on Thursday but I don’t know, we will see.”
Saturday’s draw left Liverpool in 10th place in the Premier League table after having taken 13 points from their opening nine games.
The Reds host Southampton at Anfield when they return to top-flight action on Sunday, before a trip to Chelsea at the end of the month.
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