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Rangnick is set to become the club's interim manager for the rest of the season following Ole Gunnar Solskjaer's sacking on Sunday.
The German coach has a reputation across Europe for having a clear philosophy and manner he wants his teams to play - which could be a disaster for Ronaldo.
When asked if he would sign Ronaldo or rival Lionel Messi back in 2016, Rangnick replied: "It would be absurd to think that it could work with them here [Leipzig].
"They are both too old and too expensive."
Since those comments were made, Ronaldo has won the Champions League three times with Real Madrid and moved on to Juventus and United respectively.
Messi, meanwhile, carried Barcelona for a number of years before his shock transfer to Paris Saint-Germain during the summer.
This season has seen Ronaldo be a standout performer for United despite their struggles domestically.
Ronaldo has scored four goals in nine Premier League appearances and six in five in the Champions League.
Scoring in every Champions League game so far means it's a record for a player in an English side.
Rangnick is set to stay on for two years in a 'consultancy role' at Old Trafford as the club attempt to restructure at the top.
The 63-year-old famously helped Hoffenheim reach the Bundesliga while overseeing the Red Bull system's rise, while also managing Leipzig over two separate stints.
It's an appointment that has many fans excited, but some United players are said to be 'unhappy' with how the deal was conducted.
News of Rangnick being drafted in by United emerged prior to the players actually being made aware of the situation.
There was no word from officials in person or in the United WhatsApp chat as a deal was completed very quickly.
Michael Carrick will take charge of Sunday's game with Chelsea and could be in charge for the midweek clash against Arsenal.
Rangnick currently has a role with Russian outfit Locomotiv Moscow and has visa issues to work through.
Do you think Ralf Rangnick will be a good appointment for Manchester United?
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Featured Image Credit: Coaches' Voice/YouTube & PA Images
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