The striker joined the Reds for what could become a club record £85 million from Benfica earlier this summer.
Liverpool raise the curtain to their 2022-23 Premier League campaign with a trip to Fulham tomorrow (12.30 BST).
Diogo Jota is absent with a hamstring injury, although Roberto Firmino - who started the Community Shield - is fit.
And Klopp admitted that Nunez still ‘needs time’ to adjust on Merseyside - suggesting Firmino will feature from the outset.
What’s been said
Reds boss Klopp said: “Darwin is ready but that doesn’t mean he has to start. I don’t know about that. We still have different options.
“He needs time to get used to a lot of things. He is already a real help. It went really quick. It was a proper pre-season training session for him, the first game.
“He said himself he was nervous at the beginning. From my point of view I sympathise with that a lot, it’s completely normal. You could see that, but he has settled pretty quickly.
“He’s had an impact, but the work will not stop here. He’s in the best possible place.”