Rangnick is expected to take over at Old Trafford for the remainder of the campaign before moving into a two-year consultancy role with the Red Devils.
However, The Mirror claims that Rangnick will put in a good word for Nagelsmann to become the new permanent coach, with the 63-year-old likely to have a say over who will take over next summer.
The 34-year-old only joined Bayern Munich from Leipzig in the summer, though, and his deal with the Bundesliga champions does not expire until 2026.
The Red Devils will once again be led by Michael Carrick for Sunday's Premier League fixture with Chelsea, and Paul Merson has questioned whether Rangnick is the right man for the Man United job. body check tags ::