The U.S. scored a late winner against Algeria in the World Cup four years ago that put them top of their group ahead of England and Klinsmann said the appointment of Algeria's Djamel Haimoudi for the Fonte Nova arena match made him uncomfortable.
"Is it a good feeling? No," Klinsmann told reporters on Monday.
"He is able to speak French with their players on the field, not with us, and it is a country we beat in the last World Cup.
"Sometimes I don't understand FIFA. I know it is difficult to always choose the right referee for the right games... We give it the benefit of the doubt.
"We hope it is not a concern, we know he did two games already and he did them very well. We hope he continues to referee in the perfect way."
Belgium coach Marc Wilmots played down the significance of the appointment.
"I don't think the referee is there to talk, he is there to referee," he told a news conference. "I'm not getting involved in a little game about the refs."
Klinsmann said the U.S., who surprisingly saw off Portugal and Ghana to qualify for the last 16 alongside Germany in Group G, were expecting a tough match against a highly-rated Belgian side, but had plans to keep the likes of Eden Hazard quiet.
"With Hazard and Mertens on both wings, you have extremely gifted players... You have to be super disciplined and not give them too much space. That's what we've worked on," he said.
Forward Jozy Altidore, who picked up a hamstring injury in the Americans' first group match, is available after training with the squad for the last few days.
"We have no fear at all," Klinsmann said. "I think it is going to be an exciting and hopefully entertaining match.
"We feel fresh, we have recovered well after every game so far. We feel we have just started this adventure."
Klinsmann said his side had practised penalty shootouts and was upbeat about pulling off another surprise by toppling a Belgian side who have three wins from three in Brazil.
"The World Cup for all of us is huge. You don't want to wait another four years to get into the quarter-finals, you want to do it now," he said.
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