The Athletic reports the Rangnick will sign a six-month contract before moving onto a consultancy role for two years.
The deal is subject to the approval of Russian side Lokomotiv Moscow, where he's working as their Head of Sport and Development.
Work permit issues mean Rangnick, 63, won't be in charge for the Red Devils' Premier League clash at Chelsea on Sunday.
Man United have thus shelved their bid to get Mauricio Pochettino, however, it's understood the club are still keen on making the Paris Saint-Germain boss Ole Gunnar Solskjaer's permanent successor.
Rangnick takes charge of a Man United side that's eighth in the Premier League and 12 points behind leaders Chelsea.
They secured their place in the last-16 of the Champions League under the guidance of Michael Carrick but were knocked out of the Carabao Cup at the first hurdle under Solskjaer.
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