The Reds opened their preparations for the 2018-19 campaign with a resounding win over National League North outfit Chester at the Deva Stadium.
Sturridge came off the bench to score twice for the Reds, and Klopp has said that the 28-year-old "looked really good" on his return to the team.
"I saw a lot of good things from Daniel. Impressed? It takes a lot for Daniel to impress me because I know about his quality. Very positive week and today he looked really good," Klopp told reporters. "We started playing football when he was involved. That's how it is."
Sturridge only scored three times in 14 appearances for Liverpool last season, and ended the campaign on loan at West Bromwich Albion.