Sturridge was forced off against Bayern Munich in the Audi Cup at the start of the month with a minor complaint, keeping him out of his side's final two pre-season friendlies.
The England international was quick to play down fears of a lengthy layoff, but he will sit out the season-opening clash against Watford on Saturday as Klopp wants him ready to take on Hoffenheim in Tuesday's Champions League qualifier.
"I'm pretty sure Daniel will be okay for Tuesday," Klopp told reporters, before being asked about the latest on Ings's injury return.
"Danny needs games. He looks really good in the sessions we had when he could be part 100%. There was no time for us to test him.
"Now he's ready to go, as fit as he can be. He will play tonight with the Under-23s. He is not really an option [against Watford] because he had no pre-season games."