The 19-year-old Austrian full-back impressed in the Champions League this season as he was able to dribble down the flanks at will and he harassed the Real defence by putting in several dangerous crosses into the middle.
Unfortunately for the youngster, however, he was wrongly booked for handling the ball inside the penalty area and he will miss the Champions League final against Chelsea on May 19.
He is being courted by the former La Liga champions but Bayern do not wish to sell the player who they procured from Austria Vienna in 2008 and who has now become a mainstay in the first team despite his young age. With Barcelona currently missing a first-choice left-back following Eric Abidal's absence due to illness, they are on the hunt for a promising left-back and Valencia's Jordi Alba is also said to be on their radar.
And although Alaba admitted that it would be an honour to play for the La Liga runner-ups, Rummenigge was forthright about Bayern's reluctance to sell the player.
"We are a buying club, not a selling one. Alaba is a bet on our future," he declared.
Alaba had earlier stated about the possible switch: "It's a huge honour to have my name associated with a club like Barca, but now I'm focused on the season finale."
Bayern Munich will play Dortmund on Saturday for the DFB Kopal Cup final. They will follow it up a week later with a home Champions League final against Chelsea on May 19.