The German is not pleased that his team will have a French speaker from the same country that the Americans eliminated from South Africa 2010 as their match official
The German hailed Djamel Haimoudi for the way in which he handled his two games in Brazil to date, Netherlands' 3-2 win over Australia and the scoreless draw between Costa Rican and England.
However, Klinsmann is concerned by the fact that not only is the 43-year-old official is a native French speaker, he hails from the same African nation that the Americans defeated 1-0 in a crunch group-stage clash in South Africa four years ago.
"We hope it's not an issue," the USA boss told reporters in Salvador on Monday.
"We know that he's done two games [at World Cup 2014] and he did them very well, so we hope he continues in the perfect manner in which he's performed so far.
"But is it a good feeling [having an Algerian referee]? No. He's able to speak with them [in his native language], but not with us. He's also from the country that we eliminated from the last World Cup with a last-minute goal.
"I know it's tricky for Fifa to choose the right referee for the right games but ... look, it is what it is. We accept it and we're going to be respectful during the game. We're just going to hope that everything goes well."
Klinsmann's Belgium counterpart, Marc Wilmots, was reluctant to be drawn on the issue but still argued that the identity of the man in the middle will have no influence on the outcome of the game at Arena Fonte Nova.
"I never talk to the referees," the former midfield ace stated. "They're not there to talk; they're there to referee.
"I liked seeing Howard Webb's performance in the Brazil-Chile game, when he disallowed a goal [for Hulk]. I know what the pressure is like on them.
"I played three times in the last 16 [of the World Cup] and the decisions were not always good. But I don't like speaking about the referee. Talking about this stuff is just about finding excuses before the game. Mistakes are made; that's football."
Meanwhile, Klinsmann confirmed that striker Jozy Altidore is ready to make his return to action after recovering from the hamstring injury he sustained 23 minutes into USA's tournament opener against Ghana.
"We don't know how much [of the game against Belgium] he can play but he's available and this is what we had been hoping for," the former Germany international enthused.
"The medical staff have done a tremendous job with him and just having him with us now is huge. But as to how many minutes he can play, we'll have to wait and see. He's been with the team for two or three days and been working day and night but I can't really say how match fit he is."
Regardless, Klinsmann is confident that the US, who pipped Cristiano Ronaldo's Portugal to second place in Group G, are capable of upsetting the heavily-fancied Belgians.
"The knockout stage obviously has a completely different dynamic but we made it very through a difficult pool," the ex-Inter forward reasoned.
"We're very hungry. We have a lot of respect for the Belgium side but we have no fear at all.
"I'm very positive that we have a great foundation for giving everything against Belgium. We feel free. We're recovering quickly after game and we've great team spirit.
"We feel like we've just started this adventure. It feels like the first week again. The people have welcomed us so well everywhere we've gone in Brazil.
"Everyone's so super positive with us and that's how our environment is now right now. We're looking forward to this game so much."
Indeed, Klinsmann says that he and his players are determined to provide football in the States with an even bigger boost, in light of the the unprecedented levels of support the national team is already enjoying both in Brazil and back home.
"Advancing to this stage means the world to me," he confessed. "I started this job three years ago and we've seen many things develop on many fronts, not just at the national team.
"But you get judged on what you do in the World Cup. So, for all of us, this is huge. This only comes along every four years. We don't want to wait another four years to get into this position.
"So, now it's about understanding the moment and doing everything to reach the last eight. We're going head to head with a very good team but, for these players, the sky's the limit.
"This is a big deal; there's no doubt about it. The players have it communicated to them through their families and the energy that comes from the States and the thousands of fans is great.
"You can see how the game is going in the States now. You can't stop it any more. It's growing on every level.
"Obviously, though, the national team is the pinnacle and we want to do well. We want to inspire them.
"We want to prove how good we are to them. Even when we lost against Germany [in the group stage], the American fans were everywhere; all over the stadium.
"They've given us such a buzz, so it's a cool moment right now and we want it to continue."