Rangnick is expected to be unveiled by the Red Devils as he takes over an interim basis for the rest of the season, after Ole Gunnar Solskjaer was sacked last week.
The Mirror have reported that the German-born coach has already identified his first target ahead of the January transfer window.
Rangnick reportedly wants to sign RB Leipzig midfielder Amadou Haidara, who he signed for the Bundesliga outfit when he was still in charge three years ago.
The Mali international, who has bagged two goals in 11 Bundesliga appearances this season, has previously revealed his admiration for the Red Devils.
“I like Manchester United very much and watch as many games as possible. I dream of playing there," he told Bild in 2019.
Rangnick will reportedly sign a six-month deal now before taking on a consultancy role with the Red Devils for two years.