And speaking after the 1-1 draw with Leeds United on Monday, which saw fans protesting out the front of Elland Road, Klopp was clearly annoyed with Neville's comments.
"Gary Neville speaks about 'You'll Never Walk Alone'," Klopp said. "That should be forbidden.
"We have the right to sing our anthem, it is ours not his. He doesn't understand it, anyway. It is not fair. I understand all the talk that is around but I don't talk about other clubs and you should not.
"I would wish Gary Neville would be in a hot seat somewhere and not everywhere where the most money is. He was at Man United where the most money is. Now he is at Sky where the most money is. Damn them to hell? He says that, he writes to that today? This is not okay.
"Our owners are great people, serious people, good people, reasonable people. It is not my decision. We are employees. I am a bit responsible for the relationship between the team and the supporters. It is not about me it is about the boys. I am a grown up man. We can react emotionally but we have to speak about it too."
Neville responded immediately on Sky Sports when asked if he should stop mentioning 'You'll Never Walk Alone'.
"Why," he said, adding; "I don't know why I am living in his head to be honest with you. I have no idea what he is on about. I employ 600 people and tried to keep them in a job in a pandemic.
"He is spiky, he has been let down. He cannot say what he wants to say but I can. The Klopp that I know, he hates everything about this. He has been let down by owners. And so have his players."