Dalglish, whose most recent spell at the helm came to an end in 2012, was impressed by the ex-Borussia Dortmund head coach's debut press conference on Friday.
He believes Liverpool fans will take Klopp to their hearts and liked the down-to-earth attitude he witnessed when the 48-year-old spoke to the media.
"He sounded very, very impressive," Dalglish told the club's official website. "I think supporters will need to fasten their seatbelts - they will really, really enjoy him.
"He seems like someone who is not in love with himself, which the Liverpool supporters can relate to, and I'm sure they will take him to their hearts.
"If they have heard the press conference where he's described himself as 'the normal one', that will do them fine because they regard themselves as being pretty normal."
Klopp's first match in charge of Liverpool is a testing trip to face Tottenham on October 17.