Sakho was suspended in April by UEFA for failing a drugs test, although the case was dropped by European soccer's governing body after his lawyers argued that a fat-burner used by the player was not on the list of banned substances.
The 26-year-old was then sent home from the club's pre-season tour of the United States for disciplinary reasons as he recovered from an Achilles injury.
He turned down a number of potential loan moves, according to British media reports, as the club offered Sakho a chance to rebuild his career away from Anfield.
"It's not a problem. He doesn't have to gain my trust," Klopp told reporters.
"He couldn't play football for a long time, it makes sense after a long break to think, 'How can you can get match time'?
"Now the squad is like it is, it is about making Mama fit. He isn't. He has had suspension and injury. Now we will see what happens. It's about who plays now, and then at the end Mama knows and I know. That is enough."
Sakho was linked with moves to Stoke City, West Bromwich Albion and Besiktas at the end of the January transfer window and appeared surplus to requirements at Anfield after the close-season signings of defenders Joel Matip and Ragnar Klavan.
Sakho's precipitous fall down the Liverpool pecking order raised eyebrows among fans, many of whom rated him as the club's best centre back after a series of fine displays prior to his ban last season.
"I am not silly enough to forget good performances but the rest we see," Klopp said.
"Now the squad is clear, now it's all good, we have one more good centre half. All good but for him it needs time."
Klopp also ruled midfielder Emre Can out of Saturday's Premier League clash with champions Leicester City and said Klavan would be assessed before the match.
"Maybe he (Can) will be back today or tomorrow in team training but it will not be enough for the Leicester game," Klopp said.
"Another player with problems is Ragnar Klavan. He had this really unlucky game. He had a bone bruise and a little rip, not too deep, around the knee. We don't need to stitch it but we have to wait."
(Reporting by Nivedita Shankar in Bengaluru; Editing by Toby Davis)
