The Sun says United have approached Struber over becoming Ralf Rangnick's new assistant at Old Trafford.
The pair are familiar with each other following a spell at Red Bull Salzburg, where Rangnick was the Director of Football and Struber was a youth team coach.
United are looking for a new coach after Michael Carrick announced he was leaving the club on Thursday.
Carrick had been the caretaker boss at Old Trafford, and he was expected to fall back into his role as first-team coach.
But with Carrick now gone, United are pursuing Struber.
Struber has spent the majority of his managerial career in his native Austria with spells in Salzburg's youth academy and their feeder side FC Liefering.
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