The England international did not feature in Tuesday night's 3-0 win over Derby County in the third round of the EFL Cup after picking up a strain during last week's 2-1 victory over Chelsea.
Klopp is hopeful that Sturridge will be available for this Saturday's match at Anfield, but he is not yet certain.
"Daniel made something like a final test yesterday," Klopp told reporters in today's press conference. "So he had three days without training but should be in training today.
"It depends on the training [whether he is fit for Hull], so it's not only [about] being part of the training. I think [he will be available] but we will see.
"He had a few issues after the game and didn't train, but trained yesterday. Now we have two days until Saturday and we will see who will train all of the time and is ready for the game."
Liverpool are unbeaten in their last five games in all competitions.