Midfielder Curtis Jones – born in Liverpool and a product of the club’s youth system – signed a five-year contract on Saturday.
Jones, 19, then scored his first Premier League goal on Sunday as the new champions beat Aston Villa 2-0.
“The dream is to have all the boys [from the academy],” Klopp said.
“The dream is to have a team full of ‘Scousers’. What we want to be is the sport for everybody with a Scouse soul.”
Klopp made clear he is looking for players with a certain outlook rather than judging them by birthplace – pointing to the three-year contract this week for England Under-17 winger Harvey Elliott, born in Surrey and a product of Fulham’s youth system.
“Of course, if you love football and are talented, we want you to be here,” the manager said.
Some of Liverpool’s most notable players have been locally produced, though; former England internationals Steven Gerrard and Jamie Carragher were both born on Merseyside and emerged from the club’s youth system.
More recently, Trent Alexander-Arnold has established himself as Liverpool’s first-choice right-back, also winning nine England caps.
Klopp said a number of other youth prospects are close to emulating the 21-year-old’s success and that it is a “good thing”.
“They are so humble and hard-working,” Klopp added.
“The perfect scenario is that we have these role model professionals around. If the boys follow this path with their talent, they will have proper careers.”