Moreno suffered an injury during Liverpool’s pre-season friendly match against AS Roma in St Louis.
The 24-year-old defender picked up a hamstring problem during the game and limped off.
Klopp has allayed fears over the injury suffered by the left-back, claiming that it was a dead leg.
“Alberto has a dead leg in his hamstring - that's all it is,” Klopp told The Liverpool Echo.
Moreno has been on the books of Liverpool since 2014 and will be an important player for the Reds this season.
The Spain international defender is a good player, but there are still doubts on him.
The former Sevilla man does make mistakes, and he needs to improve in order to make sure that he remains Liverpool’s first-choice left-back.
Moreno scored one goal and created 61 chances in 32 Premier League appearances for Liverpool last season.
The defender had a pass accuracy of 81% and a shot accuracy of 35%, and won 13 headers, 16 dribbles and 69 tackles.
The 24-year-old made 13 appearances in the Europa League during the 2015-16 campaign, creating 21 chances in the process.