Liverpool's first-choice left back suffered the injury during Scotland's Euro 2024 qualifying defeat to Spain during the international break, after colliding with goalkeeper Unai Simon.
Speculation quickly raged on the severity of Robertson's issue, with it widely reported that the length of his absence would depend on whether surgery was needed.
Speaking in his pre-match press conference ahead of Liverpool's clash with Everton on Saturday, Klopp indicated that Robertson would likely go under the knife – but refused to put a timeline on his recovery.
The manager said (via the Liverpool Echo): "I think the decision will go towards surgery. A little chance we can try without but all experts say surgery will be the best for the long term and that means he's out for a while. We don't know exactly how long."
Previous estimates have suggested that, in the event of surgery, Robertson could miss most of the rest of the calendar year as he recovers.
Asked about his options at left back, Klopp was hopeful about the range of options available to him, saying: "Thank god it's not only Kostas we have like that. Joe Gomez can play the position. Luke Chambers and other young boys. Young kids are really showing up."
Robertson is not the only absentee ahead of the Merseyside derby, Klopp confirmed that Spanish duo Stefan Bajcetic and Thiago remain out, while youngster Ben Doak will not play any part at the weekend due to a knock picked up on duty with the Scotland Under-21s. However, there is hope for Cody Gakpo.
Klopp revealed: "Gakpo trained once with the team so we will have to see how it goes for tomorrow. Bajcetic, Thiago out. Ben Doak is out, has a little muscle thing. Not available."