Diaz recently returned to Liverpool training in Dubai after a two-month absence following a knee injury suffered in October.
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However, the Colombian forward could now miss another three months with another problem in the same knee.
Diaz is expected to undergo surgery on a lateral collateral ligament issue following an inocuous incident in training.
"Yeah, he was not in the best possible place," Klopp told reporters after the 3-1 friendly defeat to Lyon on Sunday.
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"It's clear it's a big disappointment for all of us, for him as well.
"It was a non-situation in training, honestly - nothing, felt something.
"Didn't feel a lot next day but we wanted to be really cautious and said, 'OK, come on, let's have a look.'
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"Yeah, then the news came and it was a proper smash in the face. But that's it now."
The 25-year-old could miss as many as 17 games for the Reds between now and March, which marks a serious blow for Klopp.
However, there was better news concerning midfielder Harvey Elliott.
The 19-year-old was substituted during the defeat to Lyon but Klopp revealed it was only a false alarm.
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Klopp said: "He got a knock, but I think we were lucky. He looks fine now."