The France international saw his relationship with Klopp turn sour over the summer and was asked by the club to leave on a loan move during but turned down multiple offers to join the likes of Stoke City, West Bromwich Albion and Beskitas.
Sakho is currently behind Dejan Lovren, Joel Matip, Lucas Leiva and Ragnar Klavan in the central defensive pecking order at Anfield and it seems unlikely that he will be handed a run out in the starting eleven anytime soon due to his physical condition.
Klopp said: "He is closer but there is a big difference between match fitness and everything.
"It is not about how the player feels, it is about close I feel he is.
"It is a long, long time since he played and all the other players have not had a long break so it makes more sense if we use them."