Alaba only signed a new deal with the Bavarian giants in March but that has not stopped speculation suggesting he could leave the Allianz Arena following the arrival of Carlo Ancelotti.
United have been heavily linked with a move for the Austrian international but reports also claim that the Gunners have ramped up their interest in the player.
Former Bayern boss Pep Guardiola would also be interested in taking him to Manchester City should he become available and it looks as though a battle for his signature could be on the cards.
Alaba is valued in the region of £34million and although Bayern do not want to sell, it is thought the player himself would consider a move as he feels standards have dropped following the departure of Guardiola.
Reports also claim that Alaba would prefer a move to Arsenal over United, but the chance to link up with Guardiola again is sure to appeal.