Liverpool secured the services of Karius from Mainz in a £4.7million deal last week and it is expected that the 22-year-old will be used as the understudy for current keeper Simon Mignolet next season.
However, former Reds midfielder Hamann believes that Karius is a quality gloveman and has challenged him to usurp Mignolet as the number one choice between the sticks at Anfield, even if he is to take the step from Bundesliga to the Premier League.
Hamann told talkSPORT: "Germany has a history of outstanding goalkeepers, and Karius is very talented.
"Playing for Mainz and playing for Liverpool are two different things.
"His task is to make that step up to the next level. I was a bit surprised when I saw the photos that he has been given the no.1 shirt, but I think he will start the season as Liverpool's number one goalkeeper."