If it seems that Arne Slot is picking on Trent Alexander-Arnold in the Liverpool dressing room, it is not because of a problem between them. Quite the opposite, actually. Because the right-back had an unusual request. He wanted his manager to criticise him, sometimes in front of his teammates. He asked him to mention every time a forward beat him and to brand it unacceptable. It is a punishing approach designed to make him better. He feels that Slot, with his attention to detail and track record of improving players, can help.

There is an understandable focus on their relationship. Alexander-Arnold represented one of the great triumphs of Jurgen Klopp’s management: first his decision not to buy a right-back because he knew of a teenage talent in the ranks, then as an extraordinary creator who reshaped Liverpool’s tactics as the full-backs attacked more than the midfield, and finally as the vice-captain who inverted into midfield.

It did not escape attention that Slot substituted Alexander-Arnold in each of his first three games or that the 25-year-old was unhappy to be taken off against Brentford. It is a cause of some concern that Alexander-Arnold is in the last year of his contract at Anfield. Yet if mentions of his future can involve talk of a free transfer last summer, Alexander-Arnold voiced his own ambition: to become the toughest defender to encounter in Europe.

It may seem an identity shift. He is a wonderful crosser, a revolutionary force as the right-back who doubles up as playmaker. When he set up Luis Diaz’s second against Bournemouth on Saturday, it meant he had contributed to 100 Liverpool goals – scoring 19, assisting 81 – and at a younger age than anyone since Steven Gerrard. But he is putting an emphasis on defending. He is enjoying life under Slot and thinks the Dutchman can help with a policy of tough love.

“We talked about targets and aims and I said that I would like to be the defender that no one wants to come up against in Europe,” Alexander-Arnold said. “We agreed that he will be harsh on me. If any time an attacker gets by me and gets past me, he will call it out in meetings and individual meetings and say it cannot happen. We go through every game together and he highlights where he wants me to improve. Even in the [AC] Milan game, we had about 20 clips going through what I could have done better and the good parts as well. It is really refreshing to have a manager who will help and guide and teach me how to be better as a player. I am someone who wants to learn, someone who wants to be the best and someone who strives to be the best ever.”

Alexander-Arnold is aware of his reputation: that the better half of his game is on the ball, that he can be dodgy defensively. He disputes that. “I think that perception was perhaps harsh,” he said. “It was a big perception and it was hard to shrug off with just one good defensive game. But we have had four out of five clean sheets. That is exceptional from a backline. Defences win championships – that is the old saying – and being part of that defence means I have responsibilities to make sure my winger doesn’t get a sniff. I lay targets for every game which is how many times am I dribbled past, how many times does he get a cross, how many times [he takes] a shot.”

If Alexander-Arnold is laying targets, he could be one: for Real Madrid, who are admirers. His Liverpool deal has nine months left to run. Virgil van Dijk and Mohamed Salah are in a similar situation and have suggested they want new deals. Alexander-Arnold has kept his counsel, but there will be no mid-winter move. “I want to be a Liverpool player this season [as a minimum],” he said. “I have been at the club [for] 20 years now, I have signed four or five contract extensions and none of those have been played out in public. And this one won’t be either.”

It is a respectful approach. Alexander-Arnold could be a Liverpool lifer. Certainly he looks at his century of goal involvements and reflects: “It is good numbers. I think I am capable of many, many more.” His ambitions stretch beyond individual statistics. “I am a player who is highly motivated by trophies and winning things and being elite. So that is probably the main factor of anything, if you have a personality that is elite, who wants to win and will do anything to win, then that is what drives me.”

If there is a challenge to Slot and Liverpool to prove he can win with them, there is one goal that can only be realised at Anfield. Klopp showed some succession planning by making Alexander-Arnold vice-captain, and to a player seven years his senior, in Van Dijk. “I have always said I want to captain the club, that is an aim of mine and a goal of mine,” added the Merseysider. “Whether that happens is out of my hands.” Though perhaps not if Liverpool offer a suitable contract.