When Jurgen Klopp made the shock announcement in January that he would be leaving Liverpool in the summer, only one name played across the lips of the huge majority of supporters.

Xabi Alonso was the chosen one, a Champions League and FA Cup winner with Liverpool who had become Europe's hottest young coaching property by leading Bayer Leverkusen towards the Bundesliga and German Cup double in an unbeaten domestic season.

In the background, however, Alonso had made it known he would not be one half of what seemed to be a football marriage made in heaven, choosing instead to remain in Germany rather than take the road back to Anfield.

Step forward Arne Slot, the 46-year-old quietly building a stellar reputation at Feyenoord, regarded as having the ideal personality and footballing philosophy to take on what many regarded as the impossible job of succeeding the iconic Klopp.

Liverpool's new hierarchy of sporting director Richard Hughes and chief executive Michael Edwards had full confidence in Slot, the only contender offered the job despite Manchester United-bound Ruben Amorim also being touted.

Slot was considered calm enough to deal with the inevitable heat and scrutiny of following Klopp, while his belief in pressing intensity - bolted on to a more ordered strategy - was regarded as something that would take the best of what he had inherited and add new dimensions.

And on the night when Alonso did make a return to the technical area - albeit on the left-hand side reserved for the visitors - understated Dutch head coach Slot provided further evidence of the wisdom of Liverpool's decision.

No-one will know what would have transpired had Alonso been tempted by the pull of Liverpool, but few of a red persuasion harbour any regrets or look back with sorrow as they not only sit top of the Premier League but also at the summit of the new Champions League format as the Bundesliga side were swept aside 4-0 at Anfield.

And, with victory assured, Slot's name echoed deafeningly around Anfield, the coach too engrossed on events in front of him to acknowledge Liverpool's supporters - saving that until the end of a victory built on what is becoming a familiar second-half surge.

Alonso's name swiftly followed, he also declining to wave back out of respect to the travelling Bayer Leverkusen hordes, presumably deeming it disrespectful to be interacting with opposition supporters with his side 3-0 down, matters made worse by Luis Diaz completing his hat-trick seconds later.

He did walk towards the Kop to deliver a wave to the Liverpool fans who still adore him after applauding his own supporters, but this was a chastening night for Alonso, a night for the home supporters not to wonder about what might have been, but to revel in what they have under Slot.

Alonso did try to impart local knowledge to his players, constantly gesturing with his palms flat towards the floor calling for calm and composure. It worked a treat in a deadly dull first half but lost its impact as Liverpool ran riot once they had broken Bayer Leverkusen's resistance.

Slot has made an outstanding start at Liverpool, his almost under-the-radar approach reflected in his polite celebrations after the final whistle blows, in sharp contrast to the fist-pumping antics and wild animation of the man who went before him.

If Slot has one issue to address, it might be that he should give his half-time team talk before the kick-off as Liverpool, for their outstanding record this season, can be slow starters.

Liverpool put themselves in a tough spot as they trailed Brighton at half-time at Anfield on Saturday before winning 2-1, once again looking listless and lifeless until the spark was provided by Diaz's deadlock-breaker after 61 minutes.

In all competitions this season, Liverpool have scored 22 goals in the second half compared to 15 in the first, having 147 shots (with 66 on target) in the second half against 97 (and 44 on target) in the first.

Liverpool followed the pattern again here as Leverkusen keeper Lukas Hradecky was untroubled for 45 minutes before suddenly coming under the siege that brought four second-half goals.

Slot said: "I don't know if it was that much to do with intensity but we took more risk. They overloaded the midfield a lot and we adjusted and took the risk to play one v one all over. And you also sometimes have to give credit to the opposition.

"I would love to see this from the start, but the other team then normally has intensity too. What I like is until now we keep producing this energy and keep going to a higher gear. Preferably we would start like this from the start but, as I said, we have to give credit to the opponent."

Alonso was certainly in the mood to give credit to Liverpool, saying: "It is early to tell but I can see Liverpool have a very good balance, a very complete team.

"They work the 11 players and have the power to keep a clean sheet, which is important in the Champions League. In the Premier League, let's see. It is early to tell but it is looking good for them.

"The result is painful. The performance is more painful. We lacked some power and consistency. Defeat, accept it, congratulate Liverpool and move on. I will try to separate the pain from the result from the feelings of coming back and having love. I'm really thankful to have that reception."

Few could have a more seamless transition than Slot, with no Liverpool fans pining for the possibilities offered by Alonso any longer.

Slot does not agree that things have been easy, however, saying: "Not at all. If you only look at results, but Brighton was a difficult one, we were 1-0 behind and had to fight really hard. We have to play hard and work with really high intensity.

"Anfield is the best place to play, so every team that comes here is on the top of their game. If we can keep producing high intensity then we will keep winning and that is what we want."

And Slot's Liverpool continue to give their fans exactly what they want.