The midfielder has been so impressed with the new Red Devils manager during a number of talks with him that he is ready to make u-turn rather than leave the club on a free in the summer, says The Sun.
France World Cup winner Pogba is yet to play for Rangnick due to a thigh injury picked up on international duty at the start of November.
But the manager's vision of the future and the part Pogba can play in it at United has won over the player.
Former managers Jose Mourinho and Ole Gunnar Solskjaer could not find the key to unlock Pogba's best form for the Red Devils in the seasons following his then world record £89million move from Juventus in 2016.
Now Rangnick has started to convince the four-time Serie A winner that he can build a midfield and indeed a team around him.
Rangnick also believes Pogba could prove a galvanising force behind the scenes.
A number of cliques have started to develop in the squad but Pogba remains popular with all his teammates and he would be inspired by this new leadership role.
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