The US 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 said. "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 and he did them very well. We hope he continues to referee in the perfect way."
Marc Wilmots, the Belgium coach, played down the appointment's significance. "I don't think the referee is there to talk, he is there to referee," he said. "I'm not getting involved in a little game about the refs."
Klinsmann said the USA, who 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," he said. "You have to be super disciplined and not give them too much space. That's what we've worked on."
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 matches so far 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.
For Belgium, Thomas Vermaelen will miss out while captain Vincent Kompany will undergo a late fitness test. Vermaelen has not recovered from a hamstring injury while fellow defender Kompany's participation in Salvador's Fonte Nova arena is in doubt as he battles with a groin problem.
Kompany did train with the team yesterday but Wilmots said he will wait until this morning to see if the injury flares up again.
"There is a good chance we can make it. I know this kind of injury. I played for a year with a similar injury," he said. "We have now been working for two and a half years on the structure of the team.
"We have a fixed organisation and a core that can get results. Playing good football depends on the opponent. Maybe it's possible today."