In an interview published on Sports Illustrated's website on Wednesday, Klinsmann said he negotiated with United States Soccer Federation president Sunil Gulati for several weeks but the two sides could not agree on a written contract.
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"We couldn't get the deal done because of a couple of issues and the main issue was that we couldn't get it into a written format," said Klinsmann.
"Verbally it was done but then the paperwork started and we couldn't get it done in the paperwork process."
Bradley agreed to a new four-year contract last month and at the time Gulati refused to say whether he had discussed the position with other candidates.
But Klinsmann, who earlier this year said he was looking forward to getting back into coaching, said that he and U.S. Soccer had even agreed on a salary.
"Yeah that was the first thing we got off the table," said Klinsmann.
After the 2006 World Cup in Germany, Klinsmann had talks with U.S Soccer that broke down over the issue of how much power he would have, and the German suggested that had been the case during his latest round of talks.
"More and more coaches, if they have the position, try to be (general manager) and coach in one person. English coaches traditionally work that way," he said while declining to give details of what areas of control he was referring to.
Klinsmann took Germany to the semi-finals of the World Cup four years ago and then had a brief and unsuccessful spell with Bayern Munich from 2008. At this year's World Cup he was an analyst with ESPN television.
The United States reached the second round of the World Cup, finishing above England in the group stage, before losing to Ghana in the knockout stage.
