The 23-year-old was substituted during the second half of the Reds' 2-0 win at St James' Park on Saturday.
Nunez left the pitch holding his shoulder after an earlier clash with Newcastle defender Kieran Trappier.
"There's a chance, we have to see how he'll cope with the pain," said Klopp.
Uruguay international Nunez has scored 11 goals in all competitions for Liverpool this season after joining from Benfica in the summer.
Liverpool welcome La Liga giants Real Madrid to Infield on Tuesday (20:00 GMT) for their last-16 first leg.
It is the first time the two sides have met since last season's Champions League final in Paris, which Real won 1-0.
"I watched it back this weekend," said Klopp of that match. "I realized why I hadn't before that.
"It was torture; we played a good game, we could have won it but they scored the decisive goal. You could see their experience, how little they lose confidence, they are there for their chance. That is what you can learn from them.
"We are different teams in different times. Let's see who goes through."
Liverpool go into Tuesday's match having picked up back-to-back wins over Everton and Newcastle in the Premier League, an upturn in form following defeat by Wolves and a dismal January in which they won just one league point.
Klopp has taken confidence from his side's recent performances, and hopes they have found their form at the right time.
"It is one of the biggest games in the world [with added] recent history and it will be a top game," added Klopp.
"I am really happy we play it now. Four weeks ago it would have been different, but life is all about timing and maybe we found back our feet in time.
"Now we have these two results and hopefully we can build on that but now we need to play two super games.
"If we don't play our best we don't have a chance. Real Madrid doesn't have to play their best [to] still have a chance."
'I think they will do well' - Benitez
Speaking to Spanish football expert Guillen Balaguer on BBC Radio 5 Live, Rafael Benitez said Liverpool have what it takes to match Real.
Benitez, who led the Reds to the Champions League title in 2005 and also managed Real, said: "The difference in the past was Real Madrid used to play finals a lot of times, now Liverpool also has this experience so they will be there.
"The only problem for me is that they will have too many important games coming and now you are under pressure. You play against Newcastle and after you have to play against Real Madrid, so massive games, very important, very intensive games. Can they cope with all these things?
"I think so, with the players coming back. That is a risk. If almost everybody is fit, I think they will do well."