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.
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.
