United’s new interim manager takes charge of his first match on Sunday as Crystal Palace visit Old Trafford in the Premier League.
The German has been brought in until the end of the season following Ole Gunnar Solskjaer’s sacking a fortnight ago.
He picks up the reins from Michael Carrick, whose three-match spell as caretaker boss ended with Thursday’s 3-2 victory over Arsenal.
Rangnick told the club’s official website: “I think everybody expects, especially the supporters, but also the players, the coaching staff, to perform in a successful way and to play in style – and to combine those two things.
“I think this is the major target in the next days, weeks, months, to make sure that the fans can see what we want to play and that we do that, investing everything that we can, to get better.
“This is for me the major target in the next weeks.”
United hit a low as they were thrashed 4-1 at Watford on November 20. Coming after convincing defeats by Leicester, Liverpool and Manchester City in the preceding weeks, it was the result that proved terminal for Solskjaer’s reign.
The mood has at least lifted since with the results under Carrick – two wins and a draw in all competitions – and the appointment of Rangnick fuelling some optimism.
They will hope to add to that as they host a Palace side without a win in three games and beaten on their last trip north, to Leeds, on Tuesday.
Focus will inevitably fall on whether Cristiano Ronaldo makes the starting line-up or not. Aside from debate over exactly how he will fit into Rangnick’s plans, there is a question mark over the Portuguese’s fitness after he was substituted late against Arsenal.
Ronaldo scored twice as United came from behind to win but headed straight down the tunnel after being taken off in the 88th minute.
Former Palace right-back Aaron Wan-Bissaka is also hoping to return to face his old club after a hand injury ruled him out on Thursday.