The Reds went all out to sign the Brazil international from Roma last month, splashing out a reported £67m to finalise the drawn-out negotiations.
Klopp has already been impressed by how quickly Alisson has settled into life at his new club, and the German believes that his new number one ticks all the boxes to become an Anfield great.
"The good thing is from the first day he has been very stable and calm, but then again we already knew a few things about his personality when we signed him," he told Sky Sports News.
"And apart from catching balls, that helps massively. You need to have the right personality for that very difficult job. And obviously he has that."
Alisson is expected to make his competitive debut for Liverpool in Sunday afternoon's Premier League meeting with West Ham United.