Konate has been sidelined since the Reds' last outing in the competition, the 7-1 victory against Rangers earlier in the month, while Nunez sat out the Premier League fixture with Nottingham Forest on the weekend.
However, Thiago Alcantara and Joel Matip remain unavailable for selection.
Asked about Thiago's status at a pre-match press conference on Tuesday evening, Klopp said: "Still out.
"Yes, he [Konate] is here. Ready to play minutes, I would say. He could play the first minutes but that would not make too much sense, so minutes yes. That's it. Nothing new yet."
On Nunez’s condition, Klopp added: “He trained normal yesterday and today. So yes, in this moment, he is available."
Pressed on whether Thiago will miss the contest with Leeds United on Saturday due to his ear infection, the boss responded: "I hope not but who knows?"