With Bayern and Alaba still unable to agree on a new contract, Alaba's father - who acts as his agent - has reportedly been in contact with Barcelona to see if he can secure his son a move to Spain.
Should he move to Barca it would be at the end of his existing deal in 2021 on a free transfer.
Sport are reporting this and also say the Austria international can see himself finishing his playing career in Munich.
According to The Telegraph, Chelsea and Manchester City are monitoring the versatile 28-year-old.
THE EXPERT VIEW
Eurosport Spain's Jose Arronis...
Barcelona are exploring the market. They are looking for a left-back and a central defender.
David Alaba is a top player who can play in both positions but the problem is his salary.
Eric García (Manchester City) seems the best option, he was one of the golden boys in La Masía and already knows the club. He’s young and would learn from Gerard Piqué.
The problem is Guardiola loves him and he will be an important piece in City’s plan.
Juan Bernat of Bayern Munich - who is also linked to Barcelona - is bottom priority on the list of players Barcelona are reportedly looking at.