The federation is seeking a new national team coach after dismissing Gregg Berhalter.
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The Independent says a first approach to Klopp has been made.
Klopp left Liverpool at the end of last season - and the German has been clear that he wants to take a break from football.
However, the USA hopes to convince the German - as a national team assignment is not as time-consuming as managing a club team.
Further, Klopp would lead the national team as host nation for the 2026 World Cup.