The England international has not played since November 19 because of a calf problem and his manager has already ruled him out of their next two matches against West Ham, this weekend, and Middlesbrough.
Even then, Klopp will put no timescale on when the 27-year-old will be ready to come back — which is an issue considering Danny Ings has been ruled out for the rest of the season with knee ligament damage and Philippe Coutinho is out until the new year with an ankle injury.
“I have no idea when he will be back,” said Klopp.
“Until now he didn’t train. He wasn’t 100 per cent yesterday but he will be on the pitch today but that means starting the work. He won’t be with the team.”
Asked what he could do about it the German, who said Sturridge was “not happy” added: “Nothing. Wait. That is my job. That is the life of football. You cannot force things like this.
“He is not in training with the team at the moment so we don’t have to think about him for the team with West Ham and Middlesbrough but maybe then. What’s the game after Middlesbrough? Everton? Oh!”
Sturridge has made just 11 appearances this season, six as substitute, and his only goals have come in the EFL Cup with two apiece against Burton and Tottenham.
His latest problem is his 22nd different injury since arriving on Merseyside in January 2013.
Sturridge made just 14 Premier League appearances last season and only 12 in the 2014/15 campaign and has never made a league start for Liverpool in the month of December.
His last Premier League start in December came for Chelsea on New Year’s Eve 2011 against Aston Villa.
One player who will be in the side for the visit of West Ham will be goalkeeper Loris Karius, despite criticism being levelled at him for errors in the 4-3 defeat at Bournemouth last weekend.
“I heard the criticism was very harsh,” said Klopp. “When we analysed the game I found eight players who could have defended the (winning) goal before Loris was involved. He made a mistake too — even the best goalkeepers in the world still make mistakes.”
Meanwhile West Ham manager Slaven Bilic believes injuries have affected his side’s rhythm this season.
Bilic questioned his players’ commitment to the club and suggested there had been a loss of intensity in training following the 5-1 home defeat to Arsenal last weekend, but attempted to put the record straight ahead of tomorrow’s clash with Liverpool.
Bilic told the Evening Standard: “When I talked about the loss of intensity, some people thought I was pointing a finger at my staff. That was wrong. I think I said, four or five times, that it is me and it is my job to take responsibility. Believe me, we’re not having a jolly-up in training... it’s not like that.”
West Ham have been struggling withinjuries with Diafra Sakho (hamstring), Reece Oxford (ankle), Cheikhou Kouyate (groin) and Sam Byram (hamstring) sidelined.
“The main reason why we lost that intensity is that we have had so many injuries, all in a small space of time,” added Bilic in his column.
The Hammers have been boosted as Michail Antonio and Aaron Cresswell are fit enough to return to the squad