The 23-year-old’s contract at Paris Saint-Germain expires at the end of the season and Madrid, who failed with a £170million bid last summer, are reportedly closing in on a huge Bosman deal ahead of the summer.
PSG remain desperate to keep hold of Mbappe, who was crowned Ligue 1’s player of the season after scoring 25 goals, but reports on Monday claimed an agreement with the Spanish giants could be finalised on Tuesday.
Liverpool have long been linked with a move for the World Cup winner but Klopp was tight-lipped about any contact with the player.
"Of course, we're interested in Kylian. We're not blind," Klopp told reporters ahead of Tuesday's Premier League game against Southampton. "I have nothing to say about (the reported contact). Between Kylian and Liverpool ... it's all fine."
Klopp's comments come with Liverpool hoping to tie down Mohamed Salah to a new deal, while fellow forward Sadio Mane has been linked with a switch away from Anfield.
"We, of course, like him (Mbappe), if you don't like him, then you have to question yourself," Klopp added.
"But no, we're not ... we cannot be part of these battles. There must be other clubs involved, but that is fine. He's a great player."
A victory for Liverpool on Tuesday would leave them a point behind leaders Manchester City ahead of the final round of the campaign.