"Nathaniel is working hard on his rehab and we have kept a close eye on his progress but the reality is we are looking at some time still before he is back and available for selection," Klopp told the club's official website.
"I am told it will be longer than just a couple of weeks, so we will continue to monitor and assess."
Clyne was not named in Liverpool's Champions League squad for the group stages, which are played until December, but Klopp is confident that the 26-year-old could feature in the competition if the club progress to the latter stages.
"It is pretty certain he'll not be available for the majority of the Champions League group matches. If we are fortunate enough to still be in UEFA competition in the New Year he could be added to the squad then," the German boss added.
Liverpool's immediate attention will turn to Saturday's trip to face Manchester City in the league.
(Reporting by Aditi Prakash in Bengaluru; Editing by Clare Fallon)
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