Sakho has not played for the Reds' first team since April, when he was suspended following a positive doping test.
The case was ultimately dismissed by UEFA but Sakho was then sent home by Klopp from the team's pre-season tour to the US for breaches of discipline.
An achilles injury meant the 26-year-old was not available for the start of the season but he further inflamed things with Klopp by taking to Snapchat last weekend to claim the club were not telling the truth and that he was fit.
However, he returned to action for Liverpool in an under-23 game against Wolfsburg on Wednesday night, playing the full 90 minutes.