The Reds are one of four teams - along with Tottenham Hotspur, Chelsea and Watford - to have won each of their first three games of the 2018-19 campaign, but are the only side in the English top flight yet to concede a goal.
Klopp's table-toppers beat West Ham United 4-0 on the opening day, dispatched Crystal Palace 2-0 at Selhurst Park and defeated Brighton thanks to Mohamed Salah's 23rd-minute strike.
The trio of shutouts have been secured using an unchanged starting XI, but with a defensive unit that are playing together this season for the very first time.