The Liverpool boss heaped praise on the former England midfielder for showing the versatility to become one of the best full-backs in the Premier League this season.
Milner, 31, arrived at Liverpool in 2015 from Manchester City looking to get regular games in his preferred position of central midfield.
He did just that under Klopp and his predecessor Brendan Rodgers.
But at the start of Liverpool’s pre-season tour of America last summer, Klopp told Milner he had a new role in mind for him.
“What I can say is that I didn’t think a second until now about another left back,” said Klopp.
“We are always looking for players but in this moment we have two left backs – Milly (Milner) is one and Alberto Moreno the other.
“Our situation is this position is really comfortable. Milly is still able to play other positions.
“Left full back is a position where you can never have enough. If you’re looking for one you won’t find one.
“If you’re not looking sometimes you get one or two opportunities to have one but it is about having the right one. It is not really on the top of the things we are doing at this moment.”
Klopp has urged Liverpool fans to keep dreaming as they enter a “decisive” period of their season that could have a big say on their hopes for silverware.
The Reds host struggling Swansea today in the Premier League then face Southampton in the second leg of their EFL Cup semi-final, trailing 1-0 in the tie.
An FA Cup fourth-round tie with Wolves next weekend is followed by a huge clash in the title race against Chelsea.
And the Kop boss does not want the Reds to worry about past slip ups as he admits the title race is well and truly on.
He said: “It has started already. Until now we have done a really good job but I know it is very decisive in a moment like this, especially for Liverpool supporters.
“You don’t start thinking ‘Yes we are close but we were also close in 2008 – I have no idea when – and in the end it slipped through our fingers’. That is the wrong way to think.
“It is so positive that it allows us to dream, but the reality is we have to play Swansea, and then Southampton, and then Wolves, and then Chelsea, and then Hull and then I have no idea. That is the job we have to do.”
