The right-back had been enjoying a fruitful preseason, but will now be on the sidelines from anywhere between six months to nine months.
Klopp told Liverpool's club website: "What can I say other than how gutted we all are for Clyney. He was training and playing so well - he was in outstanding shape.
"Clearly an injury of this nature isn't a happy moment for any player, but the silver lining for him is that, according to the medical guys, it's a straightforward ACL injury. This means fixing it and coming back from it should follow a path that is free from pitfalls and complications.
"At the moment there isn't much more to say beyond we'll all support Clyney in whatever way we can and we look forward to seeing him back on the pitch as soon as responsibly possible.
"He is such a sound professional and is naturally very fit and strong, so all these things are in his favour."
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