England manager Gareth Southgate opted not to select the right-back in his starting line-up for the recent Nations League matches against Italy and Germany.
 The 23-year-old was an unused substitute as England lost 1-0 in Italy and was not even in the matchday squad for the 3-3 draw against Germany.
It means his hopes of making the squad for the World Cup starting in November hang by a thread.
Reportedly concerned by Alexander-Arnold's defensive deficiencies, Southgate appears to prefer Manchester City's Kyle Walker, Chelsea's Reece James and Newcastle's Kieran Trippier.
Klopp accepts Southgate has a different way of playing that demands more of his defenders in comparison with Liverpool's attacking approach, in which Alexander-Arnold often effectively operates as an extra midfielder.
But while Klopp acknowledges Liverpool have different tactics from England, he believes Alexander-Arnold could shine in any set-up.
"You really want to open this box? We are fine here," Klopp said on Friday.
"He is a good defender. He doesn't always defend good, that is true as well, but that is what we're working on, he is a young player.
"There is space for improvement, but we only discuss it on the level we discuss it because his offensive impact is so extreme for us. It could be for each team in the world.
"My point of view? It's an easy pick. Whichever team I would coach in the moment, I would sign him because he is exceptional.
"Is he always exceptional? No, but I have not met a player who is."
Alexander-Arnold, who missed last year's European Championship through injury, has just a few weeks to change Southgate's mind before the World Cup squad for Qatar is named.
But Klopp said the defender, a Premier League and Champions League winner with the Reds, is only focused on boosting Liverpool's title aspirations, starting against Brighton on Saturday.
"Trent came back and was not in party mood but he just accepts the decision of the manager because he understands football pretty well," Klopp said.
"He is an extremely smart boy and in football you cannot offer more than you can offer.
"For me he is a world-class player and not playing for your country is difficult but it is only because there are
other world-class players as well."