The Liverpool defender, 23, did not figure against Italy and was dropped from the squad that drew with Germany.
Reds boss Klopp says there is "space for improvement" in Alexander-Arnold's defensive game, but his offensive ability is "so extreme".
"I'd decide obviously differently, but I'm not in charge," said Klopp.
"My point of view, it's an easy pick. Whichever team I would coach at the moment, I would sign him because he is exceptional."
Southgate has said he feels Alexander-Arnold's "all-round game" is behind that of right-back rival Kieran Trippier.
Alexander-Arnold, who missed last year's European Championship through injury, has made just one international appearance this year.
He has been a key player for a Liverpool side that has won the Premier League and Champions League in recent years, but he has struggled to transfer that form to international football and has won just 17 caps since his 2018 debut.
"There are stories out there all the time that talk about him and say he's not a good defender, but that's not true," said Klopp.
"A world-class talent gets judged by the one thing he is not as world-class at as the other things. If he was not a good defender, he would not play.
"The skillset he has for being influential in possession is mad for a right-back.
"I don't know if I ever saw a right-back like this - passing here, passing there, switching sides, taking free-kicks, corners, smart decisions, quick decisions.
"He is an outstanding football player in a situation where three other right-backs in this country are doing really well. We should not forget that.
"So the view on that is how influential can Trent be? That is number one. What is he good at? That is how you judge a player."
'Alexander-Arnold was not in a party mood on return'
Southgate prefers to start with Chelsea's Reece James, who can also play as part of a back three, with Trippier as back-up, making Alexander-Arnold's chances of being in England's World Cup squad increasingly slim.
But Klopp believes Alexander-Arnold could still find a way to prosper in the current squad and has no concerns about his player's response to his latest England setback.
He added: "Trent came back and was not in a party mood, but he just accepts the decision of the manager as well because he understands football pretty well.
"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.
"England is obviously blessed with a lot of really talented players in a similar position and it's difficult to line them all up together.
"In this case, it could work. Reece James can play in a three in the back, and that would be interesting to see how they could interchange positions."
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