Sturridge will miss Sunday’s game with West Ham United at Anfield having been absent since the 0-0 draw with Southampton because of the injury.
Klopp told his pre-match press conference, as reported by the Liverpool Echo: “No idea when he will be back. Until now he hasn’t trained. He’s not with the team.
“He’s not happy. That’s the life of footballer. You can’t force these things.
“Maybe today he will go on the pitch, but that means we’re starting football work on the pitch and not with the team, with the rehab coach.
“I can’t make timelines. What’s the game after Middlesbrough? Everton? That would be nice but I have no idea.”
It looks likely that a front three attack of Roberto Firmino, Sadio Mane and Divock Origi will continue for the visit of Slaven Bilic’s side this weekend.
One man’s performance who is likely to be scrutinised closely is that of goalkeeper Loris Karius, who came in for a lot of criticism for his role in their 4-3 defeat to Bournemouth last weekend – notably when he spilled a shot that allowed Nathan Ake to score the winner.
Klopp placed the emphasis on the team, saying: “We live in a public world, everything is interesting and we have to deal with pressure. Shut your ears, I would say, it helps a lot.
“I only heard about harsh criticism. I analysed and eight players could have defended the goal before Loris was involved.”
The Liverpool manager suggested they had some things to learn from their defeat to Bournemouth last weekend, which saw the Reds surrender a two-goal lead.
“This game helped us to understand what’s wrong with our protection sometimes.
“At 3-1 up we played one bad pass and they scored. They used that situation. It was our fault. We were responsible for it.”
Klopp decided to take his players to Barcelona in midweek ahead of this Sunday’s game against West Ham both to train and rest ahead of a very busy period for the club.
“It was a wonderful opportunity the club gave us. Any person needs a little bit of rest. You can’t push them through all the time.”