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Red Bull co-owner Dietrich Mateschitz has said should RB Leipzig and Salzburg meet in the Champions League it will "remain a sporting competition."
UEFA allowed both Leipzig and Salzburg into the Champions League because it could not prove that Red Bull had "decisive influence" over both clubs.
The New Saints saw their hopes of Champions League progress dented after a 2-0 away defeat against Croatian side Rijeka in the first leg.
Changes made to comply with rules that ban clubs owned by the same entity from playing in the same competition.
UEFA will allow Bundesliga runners-up RB Leipzig to play in the Champions League next season.
Red Bull Salzburg clinched a fourth straight Austrian title -- meaning UEFA need to decide on whether RB Leipzig can compete in the Champions League.
RB Leipzig CEO Oliver Mintzlaff has said that the partnership between his club and Red Bull Salzburg is like any other partnership.
RB Salzburg won their first UEFA Youth League title with a 2-1 defeat of Benfica in the final on Monday.
Reports said the 31-year-old, who previously played for Espanyol, had signed a three-year contract with Beijing.
RB Leipzig's CEO has said "there is no nervousness" about the prospect of a ban from European competition for having the same owner as RB Salzburg.
The Vancouver Whitecaps signed attacker Yordy Reyna from Austrian champions Red Bull Salzburg on Monday.
"I'm the New York Red Bulls' coach." Jesse Marsch repeated several times that rumors of him joining Red Bull Salzburg are false.
RB Leipzig have signed defender Dayot Upamecano from Red Bull Salzburg on a contract until 2021.
The New York Red Bulls say Jesse Marsch will remain as head coach amid reports he would shift to become manager of Austrian club Red Bull Salzburg.
Upamecano, 18, has decided to make the switch to Germany, football magazine kicker reported.
Manchester United's troubles away from home in Europe continued in a 2-1 defeat at Fenerbahce in the Europa League as Paul Pogba limped off injured.
Alassane Plea's first-half strike handed Nice their first ever European away victory as they secured a 1-0 Europa League win over Salzburg.
Andre Wisdom believes his season-long loan at Red Bull Salzburg presents a good opportunity to learn a new culture and play regular football.
Manchester United laboured to a 1-0 Europa League victory over Zorya Luhansk at Old Trafford as Zlatan Ibrahimovic headed home in the second half.
The Austrian club was founded in 2005 when soft drink giant Red Bull bought and re-branded Austria Salzburg, changing the club's colours.
Martin Hinteregger rejected RB Leipzig to join Augsburg as "a matter of respect," for FC Salzburg.
Liverpool defender Andre Wisdom has joined FC Salzburg on a season-long loan, both clubs have confirmed.
Liverpool defender Andre Wisdom is set for a surprise loan move to Red Bull Salzburg, sources close to the club have told ESPN FC.