The Austrian is currently in the final year of his current deal at the Allianz Arena, with Bayern bosses keen to tie him down to an extended contract.
However, according to Bild, the latest round of negotiations didn't advance the deal any further, with the player and club still apart in salary demands.
Bayern have reportedly offered Alaba €11m per season plus another €6m in bonuses, but the player is believed to be asking to become one of the club's highest paid players, having been with the club for a decade.
That subsequently led to Alaba's father coming out and defending how the negotiations have been made from the player's camp, while Bayern Karl-Heinz Rummenigge later expressed regret that a war of words had started following Hoeness' outburst.
The 28-year-old's trophy cabinet is full to the brim due to his time with the club as he has won two Champions League titles, nine Bundesliga titkes, and six DFB-Pokal titles in his 10-year tenure in Munich.
In recent years, he has successfully transitioned from a left-back into a centre-back, and was a key player in Bayern winning the Champions League last season in 2019/20.
In January, the player will be free to talk to another club.