The Bavarian giants’ appreciation of Germany international Sane is no secret, and he has regularly been linked with a move to the Allianz Arena.
Alaba’s agent Pini Zahavi pitched the idea to the English club, who have taken it under consideration.
However, neither Alaba nor Zahavi are said to be keen on the idea.
The 27-year-old has a contract with Bayern until 2021 and wants to seal a move to Spain if he isn’t offered an extension.
Sane also has a deal running until the summer of 2021 and City run the risk of losing him for free if he doesn’t leave or pen fresh terms this summer, as he would enter the final year of his contract.
The winger has only made one appearance for City this season, in the Community Shield back in August, and has missed the rest of the campaign with a ruptured cruciate ligament.
Alaba has featured regularly for Bayern, scoring one goal in 28 appearances across all competitions.