It is understood top-level discussions have started between the club and the company about a possible shirt sponsorship agreement.
No-one involved in those discussions is prepared to go on record as to how far reaching any deal could be.
But today’s revelation is likely to prompt speculation that a stadium naming rights deal could also be under consideration.
Red Bull is already involved with a string of football clubs around the world – the New York Red Bulls and Austria’s FC Red Bull Salzburg play in grounds named after the company.
Asked whether the talks could involve a stadium naming rights deal, highly-respected brands expert Jonathan Gabay said: “It’s not out of the question.
“They would have to be cautious, because the initial reaction of football fans is to resist that kind of move. At the same time, however, I think fans are coming round to the idea that this is the way the sport is going.”
Mr Gabay added: “As a brand, Red Bull is all about the idea of excitement. They would want to be involved with a club which matches that image.”
United have made no public comment but managing director David Haigh is known to have well-placed contacts at Red Bull.
A source close to the talks said: “Red Bull are a huge brand name and a partnership with Leeds would obviously be a really exciting coup.”
Red Bull’s turnover in 2012 was close to five billion euros. The firm’s sporting interests away from football include a Formula 1 motor racing team.
Talk of a new name for Elland Road will stir memories of United’s ground move plans during the chairmanship of Peter Ridsdale.
Leeds chose a site off the A1(M) near Stourton for a new stadium and were in negotiations with a number of major international firms over naming rights before the proposal was scuppered by the club’s meltdown on and off the pitch.