The France international served a 30-day suspension - meaning he missed the Europa League final - for a failed drugs test in April which was later rescinded and was then sent home from the club's pre-season tour of the United States because of concerns over his attitude.
The defender was told by Klopp to go out on loan in August in order to show he was prepared to work to win back his place but the 26-year-old turned down moves to Stoke, West Brom and Besiktas.
"It is not a problem. He doesn't have to gain my trust," said Klopp.
"He couldn't play football for a long time. It makes sense after a long break you think about how you can get match time and that is difficult here because the other players are fit and hopefully stay fit.
"I spoke to him before the window closed because that is the moment to make decisions and that is what I did.
"Not only with Mama but with all the players I told them all what I thought would be best and now the squad is like it is.
"I am not silly enough to forget good performances but in the end we will see what happens.
"We have one more good centre-half so it is all good but for him it needs time.
"Now it is about making Mama fit - what he isn't after this long time with suspension and injury - and we will see what happens.
"I have no idea what happens when because it is who plays how, who performs when, our results.
"At the end Mama knows and I know and from my side that is enough."