Sturridge missed the bulk of last season with thigh and calf injuries which ultimately led to a hip operation and was then sidelined by a knee injury just before Klopp took over in October.
The 26-year-old then made three appearances under the German before he suffered a hamstring problem but suggested on Boxing Day he was ready for a first appearance since December 6 when he tweeted: "I'm back training and good to go!!"
Klopp, however, is refusing to take any risks with the England international and told several national newspapers: "This is absolutely the same thing that Daniel said four weeks ago, and we let him play and he was injured again.
"You ask him and he says he's good. I know he is good, but he has to train. We cannot change the situation, he has to train now.
"Last week and this week are the most intensive weeks in training for Daniel Sturridge in the last three years. So now you can see what we have to do. We cannot say, 'Come on Daniel, now you look good so you can play'.
"I don't want to see him in training because everybody sees him training and they think, 'Oh, come on, bring him into the team, we need his quality'.
"No. We really, really have to be patient now. We have to wait. We have to train. We have to give the body the right information, and if he can do this, then maybe we can change something.
"Otherwise we always have to stay here in this situation for the next 10 years and always talk about, 'Where is Daniel Sturridge, can you play him?'.
"We have to try and change something. We have tried everything else, so we must try this now."