The England international's last appearance for the Reds came during a pre-season friendly fixture in July.
Clyne is now expected to be out until February when Klopp, who has previously said the injury was not a "big problem", anticipates he will be back in his first team squad.
NATHANIEL CLYNE has undergone "successful" surgery on his back. but still faces around three months on the sidelines.
Besides Clyne's long-term absence, the Reds are also running the rule over Sadio Mane who was forced to end his worldwide duty with Senegal early last week with a suspected hamstring problem.
According to the Liverpool Echo, the full-back underwent a corrective operation in London.More news: Sen. Daines withdraws endorsement of Alabama's Roy Moore
The English media reported on Monday evening that the England worldwide has undergone corrective back surgery on an issue that has plagued him for months, and will continue to do so with the 25-year-old now set to miss another three months of action. The former has impressed for the Anfield outfit and his display saw him being called up to England's senior side for the first time.
It is the second injury setback for the Reds boss in 24 hours after Sadio Mane returned to Merseyside early after complaining of more hamstring trouble. He played the full 90 minutes for Senegal in their 2-0 victory over South Africa.