The Liverpool boss revealed that he still "does not know" if he will be able to select the Brazilian trio just two days before his team are due to play Leeds United at Elland Road.
The availability of Alisson, Fabinho and Roberto Firmino is in doubt as FIFA consider a five-day ban for players who were not released for international duty this month.
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Discussions have been ongoing this week, with no resolution in sight as a weekend of Premier League action looms.
During his press conference this afternoon, Klopp was asked when he expects to get a definitive answer on the matter.
"I have no idea," he answered. "We train later and it would be nice today if we could train with the team I want to play on Sunday."
"Bobby will not be available because of injury. The rest? No. Difficult situation, tricky for the clubs and players, we should not forget the players wanted to play. It was not possible to let them go. It was likely they have to spend 10 days in a hotel when they return."
Firmino will not feature against Leeds on Sunday after picking up a hamstring injury in the Reds' 1-1 draw with Chelsea. But his Brazil teammates look likely to be counted out of the action anyway, since the government's requirement for hotel quarantine meant Premier League teams refused to let go of players, which FIFA deems a reprehensible offence.
"When I was speaking to Arsene Wenger and a FIFA guy before international break about the World Cup plans," Klopp added. "I got notification there'd be no exemption for the players. And us three in the room agreed the players could not go [to play for their country]."
"Brazil played 1.30am this morning (UK) time, they won all 3 games and still there is a complaint."
"The real punishment is for the players," he continued. "They can't play which is what they love to do. But the clubs too. That's really not okay."
"The players love to play, that's what they do. It's really not OK, we didn't decide the players couldn't go. We're still in a pandemic. We have to be on top of that until the end of it. We get tested 3 times a week and that means we quarantine."
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