Meanwhile, Dani Carvajal is also not in contention to feature, meaning it will come down to Nacho Fernandez and either Lucas Vazquez or Eder Militao to keep Liverpool at bay.
The return leg, which will be played at Anfield, is due to take place on April 14, meaning Real will be sweating on the fitness of the defenders until then.
The highly-anticipated match will be a repeat of the 2018 Champions League final which Real won 3-1 amid drama as a tearful Mohamed Salah sustained an injury following a controversial challenge from Ramos.
The absence of both Varane and Ramos, in particular, will come as a massive setback for the 13-times European champions against the Reds.
“My motivation is at the highest level because it’s the Champions League,” said Klopp. “This has nothing to do with 2018 but when I got the draw – because it’s the first time we played Real Madrid since then – of course I remembered the game.
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“I said after that game that if somebody asked me a week later or a month later if I would invite Sergio Ramos to my 60th birthday, then I would say no. I would think about it again.
“He’s a great footballer but I didn’t like what happened that night. It was a strange night for us but it’s long ago and I cannot get that feeling back, that anger or whatever, so I don’t even try.
“We are not on a revenge tour here. I don’t believe too much in revenge, but it would be nice to get through, because it would mean we are in the next round.”