The French defender has not played since April and was sent home from the preseason tour of America after a series of incidents relating to a lack of discipline.
Sakho has also been recuperating after an injury and so has not been fit enough for selection yet in the new season.
And Klopp has revealed that he is not close to a return to action yet – and the German will be the person to decide if and when he is.
“Still working on it. Of course he’s closer to everything.” Klopp said.
“He’s still working but being match fit is a big difference, that’s all.
“We have to make a few sessions, then it’s not about how the player feels, it’s how I feel about how close the players are. It needs time.
“It’s a long, long time since he didn’t play. All the others didn’t have that long a break.
“It makes more sense that we really use the time and that’s what we’re working on.” he finished.
Sakho defied instructions from Klopp to make a loan move away from the club during the Summer. He turned down switches to Stoke City, Sunderland and West Brom.