Alexander-Arnold is regarded as one of the world's best right-backs and has become a vital part of Liverpool's team.
The local lad broke through in 2016 and has won the Champions League as well as the Premier League.
It'd take a massive fee to get him out of Anfield, but El Nacional claim Madrid are ready to test the waters.
'Los Blancos' are aware Dani Carvajal's time at the club is coming to an end with injuries piling up.
Lucas Vasquez fills in when Carvajal is unavailable, with Carlo Ancelotti aware he needs more depth in defence.
Alexander-Arnold has also played in midfield for England this month, but it's unlikely he'd be moved from his natural position at club level.
Liverpool have started this season in fine form and current sit level on points with Chelsea and Manchester United at the top of the Premier League.
They take on Brentford on Saturday evening and Klopp is aware of the challenge they'll provide.
He told Liverpool's official website: "I really admire these kind of projects, if you want. They have a really special way of recruiting players, they are brave in pretty much all the things they do.
"They had tough things to overcome; being close and not getting promoted, obviously.
"Then being on the top, then had to go to the play-offs anyway, but made their way through. That already strengthens your character, let me say it like this.
"Now they are an incredibly brave team, to be honest. Their work against the ball, the press they play, is really good. So it will really be a tough one.
"High intensity, pressing like crazy, have a playing build-up but if the other team presses then they are not shy to go a bit more direct. In all positions, really exciting players.
"In the back three is probably the tallest in Europe - all three, massive players. All these kind of things.
"So, yeah, it's a challenge. They are in a new stadium so they enjoy that as well.
"It's an interesting thing and I really respect that a lot, but of course we go there for different reasons, not to tell them how much we like what they do.
"No, we want to get the points but we know it will be a tough one."
Featured Image Credit: PA Images
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