The English champion has made a strong start to the new campaign, beating Leeds United, Chelsea and Arsenal ahead of its next match against Aston Villa.
But the Villa game is followed by an international window – including CONMEBOL FIFA World Cup qualifiers – and a tight turnaround considering the implications of long-distance travel and COVID-19 testing.
At the end of a low-key news conference ahead of Monday's (AEST) trip to Villa Park, Klopp was asked about the challenge his international stars face in the coming weeks and offered a lengthy answer.
"I really don't want to sound disrespectful," he said. "We don't know too much about what other countries are doing.
"But I think it's like how everybody at the moment wants to have your family around you. If your son or daughter said, 'I want to travel there or there', you'd say 'I'm not sure if it's right in the moment'.
"It's a little bit like how it is with the football players. You want to keep them. I don't say that this is the safest place in the world, but it is the place we know at least and we know how to deal with the different situations, different scenarios.
"Yes, I'm slightly concerned, because it's difficult to get in contact with all FAs over the world. I understand 100 per cent the demands on FAs as well, UEFA, FIFA, all that stuff, I really understand it.
"I know how difficult the situation is for everybody. But it's just not exactly perfect the information we get from some FAs. You just don't know exactly.
"Then pretty often, as a football club, you are pretty alone in these moments. We send the players away.
"The Premier League and TV broadcasters give us another challenge on top, because they just don't care.
"If our players play on Wednesday night in Peru, for example, they still think it's a good idea to let us play on Saturday pretty early. Stuff like this, these are our problems.
"If they use normal flights, they arrive Friday afternoon and we play Saturday, maybe 12-something, against Everton. It's just these kinds of things.
"In these moments as a club, you are completely alone. Supporters of other clubs say, 'What do you want? You moan constantly'. I don't moan! I know it's difficult.
"It's just I really think - and we cannot say just here in our own country - the Premier League and the TV broadcasters don't care, it's just the same.
"As a club, you are alone in this moment. You have to make sure you bring the players home in the quickest and most safe way, because nobody else is.
"It's not like any FA says, 'Here is the private plane'. This is the situation we are in.
"That's one thing. Then they arrive on Friday, we have to see and then they take a test and you get a result the Saturday. It's really tricky.
"We try everything to make it right, to make it as safe as possible. But from time to time, a little more help would not be bad."
There was one benefit Klopp could acknowledge of the international break, with Jordan Henderson "not injured anymore" and looking to now get "match fit".
"He will have minutes, I think, for England, which is a proper win-win situation," Klopp said. "I'm really happy about that."