The deal to bring Rangnick to Old Trafford as Ole Gunnar Solskjaer's temporary replacement is not yet complete, with details still being finalised between United and the German's representatives.
Rangnick is nevertheless set to sign a six-month contract after talks between United and his present employers Lokomotiv reached an agreement.
United and Rangnick were both mindful of showing respect towards the Russian Premier League side, who only appointed the 63-year-old as their managing director of sport and communications during the summer.
The former Schalke 04 and RB Leipzig manager will not take charge of Sunday's Premier League meeting with Chelsea due to work permit issues, with caretaker Michael Carrick set to lead the coaching staff at Stamford Bridge.
Rangnick will take charge until the end of the season, while United go through the process of appointing Solskjaer's permanent successor, and will then serve in a two-year consultancy role.
As The Independent reported earlier this month, Rangnick was interested in the temporary manager's job but also wanted a position at Old Trafford beyond the end of the current campaign.
The 63-year-old is being represented in the UK by Dr. Oliver Wendt, Scott Fisher, Mel Stein and Joel Macadar.
Rangnick is considered to be the 'godfather of gegenpressing' in his native Germany, having influenced the careers of Jurgen Klopp, Thomas Tuchel, Julian Nagelsmann and many of European football's leading coaches.
Some have questioned whether United's squad is well-suited to Rangnick's style, particularly after much debate over Cristiano Ronaldo's work out of possession, but Carrick insisted on Friday that the players will be able to adjust.
"Listen, there's a lot of different styles in football," the United caretaker said. "There's a group of players here, whoever comes in they can adapt. There are some really good people and human beings in the squad and I'm sure they'll look forward to what's ahead."
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