Liverpool defeated Chelsea 4-1 on Wednesday and Nunez played the full 90 minutes, but Klopp said that he left the ground in a protective boot afterwards.
"I don't know if Darwin is available or not because after 20 minutes somebody stepped on his foot and it was very painful," Klopp told reporters ahead of Sunday's game at The Emirates.
"He only took the boot off after the game because he didn't want to see it before, he knew there was something, so he left the stadium in a boot, and it was not a football boot.
"Nothing broke, x-ray clear, but swollen. We have to see if he can get this foot back in the boot or not."
Against Chelsea, Nunez was persistent in attack but failed to score, hitting the woodwork four times, including firing a penalty against the post, and while Klopp admitted that it does affect the player, he was full of praise for the Uruguayan.
"It can impact him of course, he's a human being, if it would not affect him that would be strange. The penalty he missed, that hit him, definitely," the manager said.
"I don't judge Darwin because of the crossbar moments, I judge him for the assist he had for Lucho (Luis Diaz), because it was late in the game, super decisive for us.
"That's outstanding footballing-wise, not being bothered about your own bad luck or whatever, just staying in the game."
Klopp laughed off suggestions that he had a selection headache with players such as fullbacks Trent Alexander-Arnold and Andy Robertson returning from injury, with their stand-ins Conor Bradley and Joe Gomez in excellent form.
"That's not a challenge, it's the first moment in this season that we have kind of a luxury problem, more players available for different positions than we can start, but it's absolutely no problem."
Liverpool have a five-point advantage over Manchester City in second and Arsenal in third, but City have a game in hand, and Klopp is well aware of how hard it will be to finish ahead of Pep Guardiola's side.
"I think what we learned over the years is that if you want to be around City you better win all your games because they do," Klopp said.
"They play incredible stuff and would probably consider themselves not to be playing their best season, but look where they are."
Klopp believes Sunday's trip to Arsenal will not prove decisive in the title race.
"Arsenal, they beat us, they are definitely there, they don't beat us, ask other people," he said.
"But there are so many games to come."
