"He has indicated his readiness to prolong his contract if the World Cup goes well," the DFB said in a statement.
It is the first time Klinsmann, who replaced Rudi Voeller last year following Germany's first-round exit at Euro 2004, has given any hint about his future beyond the World Cup.
The announcement came following a meeting between Klinsmann and DFB and Bundesliga chiefs on Wednesday.
"We're delighted with Klinsmann's statement," said DFB co-president Theo Zwanziger. "It's good for us to know we can plan long-term.
"But we know that everything depends on having a successful World Cup. No decision will be made before the tournament."
Wednesday's meeting followed a day after Klinsmann's bruising two-and-a-half session with some of his fiercest critics from the Bundesliga's leading clubs.
It was agreed at the meeting to re-form the old National Team Task Force to offer support to Klinsmann, and avoid further rows, in the build-up to the World Cup.
But Klinsmann refused to give way on the two biggest areas of contention, saying he would continue living in California and stick to rotating his two first-choice goalkeepers Oliver Kahn and Jens Lehmann.
The National Team Task Force was first established after Germany's poor showing at Euro 2000 and it brought good results, with Voeller leading the team to the World Cup final two years later.
Klinsmann enjoyed a good run after replacing Voeller, with the team playing attractive football in friendly internationals and during their run to third place in the Confederations Cup.
Performances since then have been disappointing, however, particularly a 2-1 defeat away to Turkey and a drab 1-0 win over China in the last two games.
As hosts, Germany are automatically qualified for the World Cup, which begins on June 9 in Munich and finishes in Berlin on July 9.
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