The England global has not featured all season because of the issue and faces a further lay-off after he had an operation on Monday, Press Association Sport understands.
"He was in a good way and then had a little setback". Klopp had earlier said on Clyne's injury, "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. That's how back problems are", he said on November 3.
"We showed him to specialists all over the world and it is not a big problem, it just needs time, that is all".
It is understood Clyne travelled to London with a member of the club's medical staff for corrective surgery on Monday.
The recovery from surgery is expected to keep him out for a further three months, with a potential return date pencilled in for February.
Liverpool are dealing with a host of injuries to crucial first-team players with Adam Lallana, Sadio Mane, Philippe Coutinho, Dejan Lovren and Jordan Henderson all nursing issues. He played the full 90 minutes for Senegal in their 2-0 victory over South Africa.
The former Southampton player injured his back during the summer, and has not featured at all this term.
Mane, whose old hamstring injury has recurred, will arrive in Liverpool on Tuesday and Klopp confirmed the forward will be assessed.