The Reds are expected to be in the mix for domestic honours in 2018-19, with a summer of big-spending having delivered a faultless start to the campaign.
Building from this point will not be easy, though, particularly when European commitments are added to a hectic schedule.
With such a workload in mind, former Manchester United star Neville has suggested that Liverpool – who made the Champions League final last season – should narrow their focus.
He told The Times: “The Champions League - if I was Liverpool, I would kick it into touch.
“I know that’s very hard to do but if they could go into February, March, April without it, I think they could have a real chance if they had free weeks.”
Klopp is stunned to learn that such an experienced figure would make such a claim, with that approach making little sense to him.
The German remains very much of the opinion that Liverpool should be seeking to remain competitive on as many fronts as possible.
He has no intention of drawing up a list of priorities with so much of the season still to come, with his approach to management seemingly standing in stark contrast to that of a former England international who has little coaching experience of which to speak.
Quizzed on Neville’s comments during a press conference on Friday, Klopp said: “How should that work? What do we do? We don’t play Champions League or what?
“Gary should come over and tell me exactly how that would work. How do you prepare a game and not focus on it? You bring your kids in the Champions League? That would be funny!
“I don’t know what he means with that, to be honest. We have to play football. A lot of people watch our games when we play Champions League and that’s our job that we do the best we can do in all these games.
“That’s what we try. I don’t know exactly what it means but to focus on one competition can only be if maybe you are already out of the competition nearly. If it’s late in the season that you see you have a chance to do that or do this and all that stuff.
“Last year, for example, we had no chance to focus on one competition because we had to qualify for the Champions League and I don’t think that even Gary Neville would have said, ‘Quarter-finals of the Champions League, let City win’.
“It doesn’t work like this. I don’t want to be too critical because I don’t know exactly how he said it but sitting in an office and talking about football is completely different to doing the job, to be honest.
“But it’s an opinion. What did he say about Manchester United in that case? The club he’s more interested in. Nothing?”
Liverpool are set to face fellow Premier League title hopefuls Tottenham at Wembley on Saturday before opening their 2018-19 Champions League campaign at home to Paris Saint-Germain on Tuesday.