Mohamed Salah's first-half goal against Napoli on Tuesday booked the Reds' passage to the last 16 as runners-up in Group C.
That means they could be drawn against Group G winners and reigning champions Madrid in a repeat of last season's final in Kiev.
In his post-match news conference, Klopp was informed that Reds supporters had told a journalist they were keen to face Madrid again, but the German insists he is not motivated by any revenge mission.
"The only thing I know is that a lot of fans would like to have revenge against PSG [for last month's loss in Paris] but we have no say in that, that's what I know," Klopp said.
"We wait for the draw, no problem, with that, until 7:55 tonight I was really not sure that we will be in the draw and now we are in it. How could I sit here and ask for any team?
"I don't care. We are second in the group, we will have an outstanding, strong opponent, that's it."
Klopp is also not thinking about the knockout phases and who could cause his side the biggest problems in the competition.
Asked who he believed were the favourites for the Champions League, he replied: "I have no idea and I don't care actually - all the others still in the competition.
"We have such a long season and until February we have around 30 games so hopefully we are all healthy and can bring a proper formation for these games!"
Liverpool owe a debt of gratitude to goalkeeper Alisson for their progress, with the Brazilian's fantastic late point-blank save from Arkadiusz Milik denying Napoli a goal that would have seen them advance instead.
Klopp was effusive in his praise for a keeper Liverpool signed from Roma in July, but also credited those in front of him for ensuring he did not have a busier night.
"It was not only one save, he had a lot of things to do - how cool, how calm he was with the ball helps us a lot in our build up," Klopp said of Alisson.
"That save was just incredible but I really think [about] how the boys were together. If we don't defend the whole pitch like we defended…he cannot make 20 saves like the last one.
"He did. [It was] incredible, unbelievable, never saw something similar, but still he needs the other boys around."