The 24-year-old right-back has helped Klopp’s side win the Champions League, Premier League, FA Cup and League Cup in recent years.
But while he has impressed with his attacking skills, Alexander-Arnold has faced some criticism over his defensive capabilities.
Neville warned that Alexander-Arnold could cost England at the World Cup as he told Sky Sports: ‘His brilliance going forward is out of this world.
‘But we’re talking about knockout football. Whether England win or lose in a World Cup is going to be down to moments.
‘A mistake – concentration. In this moment in time, I can’t see how Gareth can go into a knockout game in a World Cup playing Trent Alexander-Arnold.
‘I want this player to be the greatest right-back of all time because he’s got the ability to do that.
‘But at times at Tottenham, he looked like he could cost Liverpool dearly. In a World Cup, I think he’s giving away a penalty [for his challenge on Sessegnon].
‘I don’t think Gareth will trust him in a knockout game.’
Klopp faced the media on Friday ahead of Liverpool’s clash with Southampton and hit back at the former Manchester United defender.
‘I heard Gary Neville said something [about Trent],’ Klopp said.
‘But he’s now 24 and won quite a few finals, important games where you have to defend against world class players.
‘He was always there, defending well. I don’t know why we have this discussion.’
Speaking about Alexander-Arnold’s inclusion in Southgate’s World Cup squad, Klopp added: ‘I think with Hendo it was clear [he would be picked] and with Trent it is nice.
‘He was very pleased about the news. Who will win the World Cup? No idea.’
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