The 23-year-old striker missed the Reds' clash away in the defeat to Nottingham Forest at the weekend.
Advertisement
Liverpool travel to the Johan Cruyff ArenA to face Ajax without without Thiago Alcantara, Diogo Jota, Luis Diaz and Joel Matip.
Defender Ibrahima Konate is also unlikely to play a major role in the game having only returned to full training on Monday.
Naby Keita and Alex Oxlade-Chamberlain are both fit again, but will play no part in Wednesday's game in Amsterdam having been left out of the Champions League squad.
Advertisement
Nunez's potential inclusion is a huge boost though for the Reds as they look to get qualification on the line.
"Darwin is good. He trained. Normally yesterday and today. In this moment he is available," Klopp said.
"Thiago was not close. Is he a doubt for tomorrow? I hope not but who knows."
Advertisement
Advertisement
"We've played really well a couple of times but it's not as if we have been without problems.
"We win a game then lose two players and another who can't play for more than 20 minutes.
"Tomorrow we have enough players with us."
A victory for the Reds, or if they avoid defeat, will see them into the last-16, finishing runners-up behind Napoli, who they face at Anfield in their final Group A match.
Advertisement