Rangnick spoke for the first time as head coach of the 20-time English champions at a press conference on Friday morning and admitted that it would be difficult for the club to make the right signings in January.
Rangnick has revealed that he would be open to staying as head coach of the club beyond the end of the season, but a two-year consultancy role is also believed to be an option.
As a result, the German is expected to have a say on transfers during his time at Old Trafford, and with that in mind, Sports Mole looks at how Man United could line up if Mukiele, Haidara and Haaland all make the move to the club in 2022.
Haidara is believed to have a £33m release clause in his contract at Leipzig, and the 23-year-old could be the perfect player to complement Fred and Bruno Fernandes as part of a midfield three, with the Mali international viewed as an update on Scott McTominay in a key area of the field.
Right-back has also been a problem for Man United this season, with Aaron Wan-Bissaka struggling in that area of the field, but Diogo Dalot would have impressed Rangnick with his performance against Arsenal on Thursday. That said, it is an area of weakness for the club, and the arrival of Mukiele certainly makes a lot of sense.
Haaland would be signed to play immediately, with the 21-year-old proving his credentials at the highest level, and there is no question that he would be the first-choice centre-forward if he arrived at Old Trafford.
As a result, there could be a change for Cristiano Ronaldo, who has played plenty of his career as a left-sided forward. The 36-year-old showed that he is still capable of pressing against Arsenal on Thursday, and Rangnick has lavished praise on the fitness of the Portugal international.
Jadon Sancho is also expected to be a key player under Rangnick, with the England international kickstarting his Old Trafford career with two goals in his last three matches, while Raphael Varane and David de Gea are certainties under the new interim manager.
Luke Shaw is under pressure from Alex Telles, who has impressed in recent matches, but the England international will fancy his chances of reclaiming his spot in the side, while Harry Maguire will be hopeful that he can put a difficult spell behind him to remain captain under Rangnick.