He was initially not assigned a return date, with the club stating he would be sidelined for a "significant period of time" but it now seems likely he will remain out until the New Year.
Robertson has spoken to Klopp about his prospects and on worldwide duty this weekend, Robertson said: "I've spoken to the manager because I felt as if the settling-in period was over for me and I thought I was ready to play", he told reporters.
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Whether this latest setback for Clyne will see the manager turn to the transfer market in January, remains to be seen. Southampton return to duty as they travel to face Liverpool on Saturday, in a game that could be very interesting. "I was looking forward to the Holland game to get some game time".
It was initially anticipated that Robertson could quickly establish himself as Liverpool's first-choice left-back but that eventuality certainly hasn't transpired, with Alberto Moreno having improved significantly.
This has meant that should have Clyne returned earlier he would ineligible to play in any of the club's group stage European games.
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But the 75-year-old former vice president has powerful military connections, having served as defence and state security minister. He called for the expulsion of "the known counter-revolutionary elements who have fomented the current instability in the party".
Robertson played in Scotland's friendly defeat to Netherlands last week and said: "I was delighted to get 90 minutes".
But he has played just one Premier League game since, as well as one appearance in the Carabao Cup.
"So, in this moment all I can really say with certainty is that we will assess Sadio as soon as he lands back in the country and make decisions on what rehab and treatment gives him the best chance of being back fit and strong for the important fixtures we have coming".
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"I know I'm still in his plans and, if I work on the things he's asked me to, hopefully I'll be in the first team or closer to it".