Sturridge was deemed fit enough to be named on the bench for Saturday's disappointing 2-2 draw with relegation-threatened Sunderland but did not feature and will again be in the squad for Tuesday's FA Cup fourth-round replay against West Ham.
The 26-year-old England international has suffered a number of soft-tissue injuries over the last 18 months, which have stalled an otherwise impressive Liverpool career, as he has scored 45 goals in 73 appearances to date.
"I think everybody hopes this," said Klopp, when asked about Sturridge's chances of making an immediate impact.
"Daniel hopes it. I hope it. That’s absolutely normal. That’s what we tried to do after the last injury.
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"When we saw him in training, then yeah, you know why everybody is waiting for him."
Klopp also denied having ever criticised the former Chelsea and Manchester City striker's fitness following reports Sturridge has become disillusioned with life on Merseyside.
"That's what we have to do. It always sounds like a criticism, but it's only a description of the situation. Nothing else," the German continued.
"Everybody knew about it. It was like it was. And now it is like it is. And in this moment, it is thumbs up.
"And now if it's possible, don’t let us think about the past, and how it was, maybe now we can start.
"Why shouldn't it be possible? It's possible. And then everything will be good, and hopefully in one year, we don't want to talk about this anymore.
"I don't know if it's realistic, but we will see."