The new Liverpool coach was full of praise for the England international.
The former Borussia Dortmund trainer has replaced Brendan Rodgers in the Anfield hot seat and will be charged with leading the Merseysiders towards Champions League qualification this season.
Despite Klopp being expected to bring in a host of his own players in the next couple of transfer windows, the outspoken coach has been singing the praises of some of the existing squad at Anfield.
The German made positive comments about the likes of Adam Lallana and Philippe Coutinho, but also picked out a less unsung hero from the ranks.
When speaking about his contingent, who draw 0-0 against Tottenham at White Hart Lane on Saturday, he has special comments for Milner.
“Milner? The complete football player, the perfect professional, a machine, everything is there,” The Express quote Klopp as saying.
“I should teach them technical aspects? This is not the biggest problem in life. We don’t have to sprinkle magical dust on them – ‘And now you can play football’. They know how to play.”
Milner moved to the Merseyside club in the summer on a free transfer from Manchester City and has slotted straight into the boiler room as a deputy for the now departed Steven Gerrard.
With Jordan Henderson current on the sidelines with injury, the England veteran has been captaining the Anfield side in recent games.