Germany midfielder Can has long been linked with the Serie A champions and a report by The Guardian on Monday claimed he would move to Turin on a free transfer and collect wages of €5 million (£4.4m/$5.9m) per season.
Juve chief executive Giuseppe Marotta also said last weekend he was "optimistic about a positive end to negotiations" with the 24-year-old.
Goal reported last Thursday that Can is close to a move to the Serie A champions, although the German manager refused to confirm that information.
"No clue," Klopp replied when asked about Can's future at a news conference. "It's not important at the moment, to be honest.
"At this moment he is 100 per cent here. That's the only thing I'm interested in.
"I really have no idea, but that's not important to me at the moment."
If Can makes a farewell appearance for the Reds in Kiev, it will be one that looked unlikely until recently.
"It depends on his reaction [to training]," Klopp explained when discussing Can's chances of featuring against Madrid.
"Ten days ago I didn't think it was possible that he could do what he did today and that he could do what he did in Marbella.
"It looked good, really positive, but we have to wait again until tomorrow. The door is open. It's really nice to have him back in the group. He is really desperate to be part of the game."