Milner turned 37 earlier this month and has started in just seven of his 21 appearances this season.
He is out of contract in June having signed a 12-month extension last summer but his influence in the dressing room cannot be under-estimated and Klopp admits they are preparing a number of options, which could include a coaching role, come the end of the campaign.
“We have different plans for Milly but Milly wants to keep playing,” said Klopp.
“When you see him play the other night (in the FA Cup replay victory at Wolves) I think everyone understands that.
“You can’t judge him normal for his age. He is 37, doesn’t look a day like this when he is in training. He is an incredibly important player and in this game (Wolves) you saw that on the pitch as well.
“It is not that Milly expects to play 64 games a season but in 64 games a season Milly could be extremely important. That is how it is. Milly has reached 600 (Premier League) games and most of them for Liverpool.
“I am pretty sure the club should use his character and his mindset because it is really special.
“There might be more fancy players out there but no one with a similar mindset and that makes him incredibly valuable for us. And it is not because I am too loyal. It is just a fact.”
There might be more fancy players out there but no one with a similar mindset and that makes him incredibly valuable for us
Klopp on Milner
Forward Roberto Firmino is also out of contract in the summer but his future appears more uncertain.
Klopp would like the Brazil international, who is currently injured, to stay but the 31-year-old would probably have to accept reduced personal terms to extend his stay at Anfield into a ninth season.
“What could be the reason? When you think a bit, where could it hang, could be the time (length of contract), the money, it is completely normal,” said the manager when asked why a new deal had not been signed.
“Bobby knows the situation here and what we think of him.
“The first part of the season we were not flying but Bobby was the only one who played a normal season.
“He is really important, the link-up, in tight areas having a player with his footballing intelligence, you can develop the game from here.
“He is unselfish and you don’t get that very often. Great player.
“I don’t know 1,000 percent what his plans are, maybe someone else will offer him something better?”