According to The Sun, the Red Devils remain supportive of their former player despite losing four of their opening nine matches this season.
33-year-old Hurzeler has impressed at Brighton, guiding the Seagulls to consecutive eighth-place Premier League finishes while establishing a strong record against United.
However, appointing the German would prove expensive after he signed a contract extension until 2029.
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Brighton owner Tony Bloom has indicated the club are prepared for potential approaches.
Other managerial options reportedly include Andoni Iraola, Oliver Glasner, Antonio Conte, Kieran McKenna and Eddie Howe.