Germany's young guns demolished England 4-1 in the second-round after topping Group D, looking slicker and sharper than the more-fancied side ahead of the tournament.
"We are very pleased from a German perspective. They are a very young team who have done very well so far," said Klinsmann, a member of West Germany's World Cup winning squad in 1990.
"We had a little set back against Serbia in the group match but then they came out strong again and for us Germans it means a lot to beat England in a knock-out game."
The squad, beaten by Serbia 1-0, features players such as Lukas Podolski, Miroslav Klose and Bastian Schweinsteiger who Klinsmann led to a surprise third place finish in the 2006 World Cup in Germany, alongside gifted newcomers such as Mesut Ozil.
"We will see how they do against Argentina and how far this team can go. They are lacking maybe a little experience and will be playing some of the best players in the world. This will be a new benchmark for them," he told reporters in Cape Town.
Joachim Low, Klinsmann's former assistant coach, took over from his former boss after the World Cup and led Germany to the Euro 2008 final where they lost to Spain.
Klinsmann said he had visited the German team on Thursday night in Cape Town and had a glass of wine with them.
"They don't need my advice ... just look at the front line the Argentines have. They know that and they know they have nothing to lose," he said at Cape Town's City Hall.
"But there could be a moment of magic and they hit them at the right time. World Cups are all about timing," he added.
Saturday's quarter-final clash between Argentina and Germany will be a repeat of the 1986 and 1990 World Cup finals, the first won by Diego Maradona's team and the second by a German side including Klinsmann.
Both teams met again at the 2006 World Cup quarter-final, when Germany went through on penalties and the match ended in an unseemly brawl.
Asked about his future, Klinsmann, who was sacked as Bayern Munich coach near the end of the 2008-09 Bundesliga season, said he would wait to see after the tournament.
"After the World Cup a lot of teams will think about their future, but for now we are all just following the World Cup," he said.
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