Nunez suffered a shoulder issue during Sunday’s 2-0 win at Newcastle United forcing him to be replaced in the second half.
Liverpool boss Jurgen Klopp expressed his concern about the Uruguayan after Sunday’s game but offered a more positive update on Monday.
“There’s a chance,” Klopp told reporters. “From all the possible scenarios, apart from being absolutely nothing; that’s not the case.
“We have to see how he can deal with the pain (and) when we know that, we make a decision.”
Nunez has netted 11 goals in 28 appearances in all competitions for the Reds this term.
Tuesday’s clash with Real is yet another iteration in their rivalry that has extended throughout many Champions League match-ups.
The encounter comes after back-to-back Premier League wins for Liverpool, who have struggled this term.
“We still have to prove that point, so that’s how it is,” Klopp said when asked if Liverpool were looking more like a team again.
“Now this is a different competition and whatever we can take, but after that it’s Crystal Palace. So, we need results, there’s no shadow of a doubt.
“We were already in a similar situation, I don’t say performance-wise but result-wise we were in a similar situation directly after the World Cup break.
“I think with the two wins, it looked like, ‘Oh now we are there.’ So, we have to prove that point. But you are right, it looks different we feel it, we see it, it helps the mood massively and from here we have to go. That’s how it is.”