The 63-year-old German is poised to join United but will not be in charge this weekend against Chelsea while he waits for his work permit.
United have agreed terms with Rangnick, but not with Lokomotiv Moscow, where he is the head of sports and development.
It comes after United sacked Ole Gunnar Solskjaer on Sunday following a trophyless three-year spell as boss.
Rangnick won the German Cup with Schalke in 2011 and took RB Leipzig to the final in 2019.
During the 2010-11 season he guided Schalke to the semi-finals of the Champions League, where they lost 6-1 on aggregate to United, who were then beaten by Barcelona in the final.
United are eighth in the Premier League and Solskjaer, who scored the winning goal in the 1999 Champions League final for the club, was dismissed following an embarrassing 4-1 loss at Watford on Saturday.
Since then, caretaker Michael Carrick, Solskjaer’s assistant, took charge of United on Tuesday for the 2-0 win at Villarreal, a result that ensured they would finish top of their Champions League group.