The England worldwide has not featured all season because of the issue and it is understood that he will face a further lay-off after having an operation on Monday.
"First and foremost, I have to say big congratulations to Senegal on the achievement of qualifying for the World Cup; this is fantastic news for their country and the players - Sadio included", said Liverpool boss Jurgen Klopp, speaking to the official website.
It is understood that Clyne underwent minor corrective surgery on his back on Monday and that he could now be unavailable to Klopp until as late as February.
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Clyne is yet to play this season and has been suffering with the back problem for some time now.
Liverpool do not need to go chasing a right-back in the January transfer window.
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Mané, meanwhile, has been released early from worldwide duty after picking up the problem during Senegal's 2-0 World Cup qualifying win over South Africa last Friday.
"At this stage we haven't seen Sadio yet to properly assess the extent, but what is clear is that we will have to stay on top of this for the rest of the week and make sure we are careful in how we look after him".
"In his case because it was a little sign again from the back, we took him out and it's a few steps back again".
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The England worldwide is, however, pencilled in to play some part in a behind-closed-doors friendly at Melwood on Tuesday.