The American has just led St Pauli to promotion to the Bundesliga.
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Just 31, Hurzeler has just secured a UK work permit as talks advance with the Seagulls.
Brighton are seeking a replacement for Roberto de Zerbi, who resigned at the end of last season.
Texas-born Hurzeler has been with St Pauli for 18 months and is a former Bayern Munich and Hoffenheim player.
He visited Brighton last season to study De Zerbi's methods.