The 29-year-old had started all of the manager's six opening games in the charge, wearing the captain's armband in the absence of the injured Jordan Henderson, until a hamstring problem ruled him out of last Sunday's game against Crystal Palace.
Milner is optimistic on his chances of recovering in time to face Manchester City on Saturday and has explained why there is still plenty he can take from Klopp's methods.
"You can always learn whether you are 16 or 17, or whether you are 35 or 29," he told Liverpoolfc.com. "That's football and the manager will still be learning himself.
"Obviously he has come in with his new ideas, new training methods and things like that, so it's great for me as much as it is the younger guys. Hopefully I can help those younger guys, but I'm still learning myself. Changing managers is always different and I'm still learning the way he wants to play.
"I've been fortunate to work under some great managers and he is another one of the top managers in the game. I can learn as much as I can and hopefully put that back into my game, as a team member and as an individual and improve."