The 49-year-old managed the three-time world champions - currently led by his friend and former assistant Joachim Low - between 2004 and 2006, but since 2011 has been in charge of the Stars and Stripes.
"[This fixture] is something that doesn't happen every year and probably not any more in a lifetime," Klinsmann told reporters.
"So you try to enjoy this moment. There is no doubt it's a special moment because it's the team that you start building, the group of people that you start to gather round and they're all in place still."
Both teams are currently on four points ahead of their final Group G game in Recife tomorrow.