The German replaced Ole Gunnar Solskjaer in November until the end of the season.
And according to ESPN, Rangnick highlighted United’s midfield as a key area to improve when being interviewed.
His shortlist include Borussia Dortmund’s Jude Bellingam, 18, Leeds star Kalvin Phillips, 26, and RB Leipzig’s Amadou Haidara, 23.
Bellingham’s Dortmund team-mate and long term United target Erling Haaland, 21, was also mentioned by Rangnick.
But both Bellingham and Haaland are among the hottest properties in Europe with the duo expected to be pursued by a number of clubs.
Hopes of landing Haaland have taken a blow however, with his agent naming Man City as a better option.
Fred, 28, and Scott McTominay, 25, started in Rangnick’s first game in charge – a 1-0 win over Crystal Palace last Sunday.
Fred scored the winner and the Brazilian won praise alongside midfield partner McTominay, but Rangnick admitted improvements could be made.
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He said: “They did one or two or three mistakes, especially in the first half there were two square passes; one from Scott, one from Fred.
“I don’t like those kinds of balls in midfield in those positions.
“But overall, when the other team is in possession of the ball, both Fred and Scotty they are almost perfect for that kind of football.”
Rangnick is expected to be backed in January but has also been told to expect a quiet window.
The manager also gave teenagers Charlie Savage and Zidane Iqbal, both 18, senior debuts.