Frank Lampard has already boosted his attack for the 2020/2021 with the additions of Werner and Hakim Ziyech but he is now looking to improve the defence.
According to English publication the Athletic, the Blues have approached the Bundesliga champions for a possible deal for their star left-back.
Despite being an integral part of the Bayern squad over the past few seasons, Alaba's contract expires at the end of next season and the club could cash in on his services now rather than risk losing him for free.
The Blues were previously linked with Leicester City left-back Ben Chilwell, but the club's reported asking price of £70million has put the Blues off.
Alaba, who can also play in midfield, has featured in 27 of Bayern's games this season on their way to securing an eighth Bundesliga title.