The Egyptian winger scored 44 goals for Liverpool across all competitions in 2017-18, including an unprecedented 32 in a 38-game Premier League campaign.
Salah has two goals in three games so far this season too, and Klopp believes that he is now playing with more confidence and maturity than he was last term.
"Mo is a very smart person. He's not thinking about the end of last season, he knows our game here, he knows he had no number in his mind or thought, 'OK, let me score a new record,'" Klopp told reporters.
"It was only ever, 'Let's score goals. Let's play football'. And to me he looks like he is exactly in that mood again... only with more confidence, because now he knows it's possible. But that is the only change. We need him to score goals but not overly. And that's how it looks from him.
"He's not a kid any more and he doesn't expect that everything will be like this all the time. If it is not like that any more, then he will dig deep, he is completely settled."
Liverpool will look to make it four wins from four in the new Premier League season when they take on Leicester City in today's early kickoff.