The Brazilian number one became the most expensive goalkeeper of all time when Liverpool brought him to Anfield last month, although that record has already been surpassed by Kepa Arrizabalaga's move to Chelsea earlier this week.
Alisson is expected to make his competitive debut for Liverpool during their Premier League opener against West Ham United on Sunday, and Klopp has been impressed with the start he has made at the club.
When asked what the 25-year-old needs to do to make an impact on the Premier League, Klopp told reporters: "Just be yourself in this case because he is a very calm person, very laid-back during the week.
"He is completely different on the pitch but around the pitch he is like that. Being a Premier League player you need to tick a few boxes; as a goalkeeper it helps if you are calm. It's about making the right decisions in the right moment.
"He has settled really quickly. He has been in for two weeks [but it] looks like he has been in for much longer."
Alisson featured twice in pre-season for Liverpool, against Napoli and Torino.