Rangnick is due to take over as manager of the Premier League side until the summer after the 63-year-old will move into a consultancy role on a two-year contract next summer.
He has a good knowledge of Bundesliga players due to his time at RB Leipzig and it has been suggested a reunion with Amadou Haidara is on the cards.
Rangnick took him from RB Salzburg to Leipzig in 2019 and the 23-year-old defensive midfielder has previously said he would love the opportunity to play for 20-time English champions United.
In 2019 he told German newspaper Bild: "I like Manchester United very much and watch as many games as possible. I dream of playing there."
The Mali international was signed as a replacement for Naby Keita, who joined Liverpool in 2018 and, while he is known for his defensive capabilities, he can also play as a box-to-box midfielder, which could work well in Rangnick's preferred '4-2-2-2' formation.
However, Newcastle are also interested in signing the player, who has a £33m release cause in his contract.
United are on the look out for a defensive-minded midfielder to provide competition for Scott McTominay and Fred.
The pair have been criticised for their inconsistency in the heart of the midfield and a recruitment in that position is seen as a priority for the Old Trafford hierarchy.