The Austrian superstar, 28, is out of contract at the Bundesliga champions at the end of the season after over a decade at the club.
Alaba and Bayern have been locked in contract talks since the summer.
The versatile star refused to put pen to paper on a new deal as he felt he was being undervalued.
Alaba currently earns around £150,000 per week at Bayern Munich - miles off the likes of Robert Lewandowski (£375,000) and Thomas Muller (£300,000).
The German giants offered Alaba a significant pay-increase - at around £200,000, according to BILD - but the Austrian still felt let down.
But the defender refused and after trying 'everything' to convince him to stay, Rummenigge has revealed the player can now negotiate pre-contract terms with any club in January.