The German could be in the dugout for Thursday's Premier League clash against Arsenal depending on how quickly he receives his work permit.
Rangnick will lead the team for the rest of the season before taking on a two-year consultancy role at Old Trafford, with the 63-year-old expected to be involved in picking Ole Gunnar Solskjaer's permanent replacement.
With that in mind, Sports Mole picks out three players that Rangnick could attempt to bring to Old Trafford in the early stages of 2022.
Amadou Haidara (RB Leipzig)
Haidara has allegedly emerged as a transfer target for Man United, with the 23-year-old believed to have a £33m release clause in his current deal with Leipzig, which certainly makes him an attractive proposition.
The central midfielder was signed by Rangnick for Leipzig from Red Bull Salzburg in 2018, and he has made 100 appearances for his current club in all competitions, contributing 10 goals and six assists in the process.
Haidara's high-energy style would make him perfect for Rangnick's brand of football, with the German expected to demand that Man United press higher up the field in a bid to regain the ball as quickly as possible when they concede possession.
The Mali international has again been a vital player for his Bundesliga club this season, scoring three times in 17 appearances, and the fact that he could be available for £33m makes him a very interesting prospect.
Man United are short of an extra body in midfield, especially considering the uncertainty surrounding Paul Pogba's future, and Haidara could be a very smart signing for the 20-time English champions.
Barcelona are, understandably, desperate to keep hold of Ousmane Dembele, but the France international's current deal at Camp Nou is due to expire next June, and the Catalan giants will have a serious decision to make in January if they continue to struggle to sign him to an extension.
A recent report claimed that Man United have identified Dembele as a leading target, and the World Cup winner is believed to be open to the idea of making the move to the Premier League.
The 24-year-old has struggled with a number of injury problems during his time at Camp Nou but has still managed to contribute 30 goals and 21 assists in 121 appearances in all competitions.
Barcelona will be wary of losing the Frenchman on a free transfer next summer, and it is not impossible to imagine Rangnick pushing to sign the former Rennes youngster, who could become a star in the Premier League if he manages to put his injury problems behind him.
Nordi Mukiele (RB Leipzig)
The right-back spot at Old Trafford has become a problem, with Aaron Wan-Bissaka largely struggling to impress since arriving from Crystal Palace. Rangnick will want his full-backs to push forward and contribute in the final third, so it would not be a surprise to see a new right-sided defender arrive in 2022.
Nordi Mukiele only has little over 18 months left to run on his contract at Leipzig, and it has recently been suggested that the 24-year-old is a target for Man United.
Rangnick was involved in the France international's move from Montpellier to Leipzig in 2018, so the new Red Devils interim manager will be more than aware of the defender's talents.
Mukiele has made 126 appearances for his current side in all competitions, contributing 10 goals and seven assists in the process, while he has been in impressive form this term, scoring twice and providing one assist in 18 outings.
Man United would not have to pay through the roof for the Frenchman, and he is certainly a player capable of thriving in Rangnick's high-pressing brand of football.