While Milner travelled with the Liverpool squad for their pre-season training camp in Germany, Klopp has ruled the left-back out of contention until the Reds return to Merseyside.
The German also conceded that Ward, Karius and Clyne were all still struggling with their own fitness issues.
“It was clear from the first day there’s a little bit of tendon involved, so that means that it’s around 10 days,” he said of Milner.
“That means he will do his rehab here in Germany and then should be fit again when we’re at home.
“With injuries, you can’t be sure but it shouldn’t be much longer.
“This is maybe the longest Clyney has been out with a little bit of [an issue with] the back. We have to wait, time is running and we need Clyney of course.
“Loris and Danny, I am not 100 percent sure. Wardy is not too serious but it always takes its time, we will see how long it takes.
“Loris should be in tomorrow or the day after tomorrow at the latest, then we will have him back but it’s not too cool for the boys.”
Klopp is, therefore, only currently training with a 26-man squad in picturesque Rottach-Egern, as he prepares his side to take on Hertha Berlin on Saturday.
The 23-year-old joined in an £8 million deal last week, and is set to make his first appearance for Liverpool at the Olympiastadion this weekend.
Furthermore, Trent Alexander-Arnold can be expected to start in place of Clyne, who has so far made just appearance throughout pre-season, in the 4-0 win away to Tranmere Rovers.
Without both Karius and Ward, Simon Mignolet is able to continue his stretch as Klopp’s undisputed first-choice goalkeeper, with youngster Kamil Grabara travelling in reserve.
Emre Can is also available, having reported back to Melwood at the weekend after his summer break.