"I had 15 months with Ilkay Gundogan (at Borussia Dortmund) where we had to all wait but it was his back and we had no chance to force it. It's not a back problem with Daniel but it's the muscle," Klopp told reporters.
Liverpool strikers Danny Ings, Divock Origi and Sturridge are all struggling with injuries, leaving Christian Benteke as Klopp's only fit experienced front man.
"Out of responsibility, we have to do everything we can to give him (Sturridge) the physical strength to be able to play Premier League football. We all know it's pretty easy for him when he's fit but at this moment he isn't."
Klopp ruled the England international out of Saturday's Premier League trip to Norwich City and the League Cup semi-final second leg against Stoke City at Anfield on Tuesday.
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Benteke has struggled to nail down a regular starting place since Klopp replaced Rodgers at the Merseyside club in October despite being the club's leading scorer with seven goals.
There are growing concerns over his suitability for the team's high-pressing style of play but Klopp praised the 25-year-old Belgian's performance in Tuesday's 3-0 FA Cup third- round replay win over fourth tier Exeter City.
"Sometimes he tried too hard, but he stayed cool and everybody could see he knows where the goal is," Klopp said.
"You need a striker who makes a goal, but you cannot wait for him to come. I have seen him playing like this, holding the ball up for the team, and we have to work hard for him to do this."
(Reporting by Shravanth Vijayakumar in Bengaluru, editing by Ed Osmond)
