Barnsley were seven points from Championship safety when Struber arrived at Oakwell in November 2019.
The Tykes then picked up six points in their final two games of the 2019-20 season, scoring winning goals in injury time against Nottingham Forest and Brentford to dramatically secure survival.
He left the club last autumn for New York Red Bulls with the club in the Championship relegation places.
The 44-year-old enjoyed a 13-year playing career before moving into management in 2009. During his playing days, he won the Austrian Bundesliga and the Austrian Super Cup.
He spent a number of years coaching in the Red Bull Salzburg academy while also spending time in charge of Austrian side SV Kuchl.
He worked with Man United's newly-appointed interim manager Ralf Rangnick at Salzburg, which is one reason the Red Devils are reportedly keen on bringing Struber to Old Trafford.
Struber had spells in charge of FC Liefering and Wolfsberger AC in the Austrian Bundesliga, leading the latter into the Europa League before opting to make the switch to Oakwell.
After a difficult start to the 2020-21 season with Barnsley, Struber was appointed head coach of MLS side New York Red Bulls in October 2020.
He has a 37 per cent winning record in the MLS. His win percentage was over 50 per cent with Wolfsberger while it sat at just under 36 per cent with Barnsley.