The Austrian international has confirmed he will not sign a contract extension when his current deal expires at the Allianz Arena in June.
The 28-year old has been heavily linked with a move to the Spanish capital in recent weeks, and according to reports from Mundo Deportivo, the two parties are on the verge of clinching a deal.
Alaba is set to complete a medical in Madrid next month, when the 2020/21 Bundesliga season finishes, and a deal could be wrapped up before the start of this summer’s European Championships.
Zinedine Zidane is confident of avoiding any last minute delays to the move despite rumoured late interest from Manchester City and Paris Saint-Germain.
Alaba leaves Bayern with an impressive haul of 10 Bundesliga titles and two Champions League wins across 12 seasons in Bavaria.