The 46-year-old led Germany to third at the 2006 World Cup and had been in discussions to take charge of the US team after July's tournament.
After negotiations broke down, US coach Bob Bradley, who led the team to the Round of 16 in South Africa, has had his contract extended.
"We had conversations, maybe about three or four weeks period of time, and very positive conversations. But we didn't get it to a positive ending because we couldn't put into writing what we agreed to verbally," Klinsmann said in an interview as part of pre-game show for Major League Soccer, according to the New York Times.
Klinsmann revealed the negotiations broke down because of the position's responsibilities.
"Verbally we agreed on that the technical side is my side, and I should have a 100 percent control of it," he said.
Having been fired by Bayern Munich in April 2009 after just nine months in charge, Klinsmann has returned to California with his family.