Founded in 2009, Leipzig are bankrolled by energy drinks giants Red Bull and are currently top of the Bundesliga after four promotions in seven years.
Impressively, they have done it with a squad without superstars and an average age of 23.
Eight of the players who started Saturday's 2-1 win over Schalke played for RB in the second division last season.
Rangnick, 58, became sports director in 2012 when Leipzig was in the fourth division.
He showed the door to those the wrong side of 30 signing youngsters on their first or second contracts, including current club captain Dominik Kaiser.
And Rangnick shakes his head when asked if he would like to sign Real Madrid's Ronaldo, 31, or Barcelona's Messi, 29.
"It would be absurd to think that it could work with them here," said Rangnick with a grin.
"They are both too old and too expensive."
His most recent recruits illustrate the point with Scotland winger Oliver Burke, 19, signed from Nottingham Forest, Guinea midfielder Naby Keita, 21, and Brazilian defender Bernardo, 21, both from sister club RB Salzburg.
"We have the youngest team -- and most unexperienced -- in the league," he said.
Rangnick admits the success of RB Leipzig -- the only club from former East Germany currently in the Bundesliga -- has caught him by surprise.
"I don't know if it's a revolution, but it's unusual that a team, who was in the fourth division three-and-a-half years ago is now on 33 points after 13 games," he said.
"Nobody expected this."
Leipzig are unpopular with some German fans, who say the team only exists to sell Red Bull's drinks.
Dortmund CEO Hans-Joachim Watzke described RB Leipzig as 'performing cans', words he may regret now as Dortmund lost 1-0 at Leipzig's Red Bull Arena in September.
"If that was true, then 11 'cans' beat 11 'bottles', which in German (slang) means 'someone who played poorly' - I say that with a twinkle in my eye," said Rangnick with a grin."
Rangnick has been here before.
He was coach of Hoffenheim in 2008/09, who are bankrolled by a German software billionaire, and were also unpopular until they beat Bayern to first in the league table by Christmas, only to eventually finish seventh.
"Whenever a new club comes along, fans of rival teams see them as an opponent and an enemy.
"It was the same with Hoffenheim, we were disliked in the second division, but really disliked when we went up to the Bundesliga.
"Then we played Bayern and we were top, and everyone was supporting us.
"There are people, not just in Leipzig, who think we deserve what is happening to us right now.
"Neutrals will say we deserve what we have with such young players."
Rangnick is seen as one of Germany's most talented managers.
He was sounded out about becoming England manager when Roy Hodgson stood down after Euro 2016 before Sam Allardyce's ill-fated 67-day reign.
"I still think it was an honour that they asked a German coach if I was available," he said.
"But even if they had offered it to me, I wouldn't have stopped working for Reb Bull completely.
"We are building our own tradition and writing our own story right now."
Rangnick rejects the notion that Leipzig are Germany's version of Leicester City, last season's surprise Premier League winners, "we share the first three letters in our names, but little else".
"In a normal season, Bayern will win the title, but maybe this isn't a normal season.
"Our match against them (December 21) won't be decisive, but it will be exciting.
"Last season, we were the favourites in each (second division) game. This season we have nothing to lose."