The former England international is set to part ways with the Reds at the end of his deal after signing for the club in 2015.
Milner appeared 43 times for Liverpool in his last campaign, coming on as a substitute in the majority of them.
Klopp described managing Milner as both a joy and a challenge and the Reds manager hailed the 37-year-old for his preparation efforts for a game.
The Liverpool boss admitted that it was difficult when Milner did not start games for Liverpool, explaining that he has never seen a larger mood change in an instant because of not starting games.
But, according to the German, that was not a problem for long, as the midfielder played a lot of games for the Reds.
Klopp told Liverpool’s official site: “A pleasure and a challenge.
“In the same moment [it] means a pleasure because of his exceptional attitude, really.
“I think for a lot of experienced players you use from time to time the word ‘role model’.
“But Millie is the role model, how he puts himself pretty much in place to be every day 100 per cent ready.
“It’s a pure example; absolutely outstanding.
“[It was] a challenge because especially in the beginning everything was alright when he was starting, but when he didn’t start then that was a bit tricky.
“I never saw a bigger mood change in an instant! Similar to Lucas Leiva, I would say.
“But he played a lot of games so he didn’t have that problem now too often, but no, really, really, really good.”
The versatile midfielder made 332 appearances for Liverpool, scoring 26 goals and assisting 46 times.
