The Red Devils have won just two games from 11 played so far this season under Michael Carrick and Hurzeler had been flagged as an early option to replace him after an impressive start to the campaign at the AMEX Stadium.
However, reports from talkSPORT indicate the German coach will reject any offers, as he remains under contract with the Seagulls until 2029 and United may need to pay £20M in compensation to bring him to Old Trafford.
Julian Nagelsmann is also on the rumoured shortlist, after stepping down from the Germany job after the 2026 FIFA World Cup, with fellow free agents Antonio Conte and Eddie Howe also in the running.
Carrick is expected to remain in place for United's Premier League clash at home to Bournemouth on October 25th, but a call on his future should be made before the November international break.