The 58-year-old, who lifted the English top-flight title and FA Cup during his two years at Chelsea, is currently under pressure at the Allianz Arena.
A disappointing pre-season campaign and a stuttered start to the Bundesliga season has seen the Italian's job called into question, with suggestions that Bayern could trigger a break clause in his three-year contract.
Ancelotti has been in charge of the Bavarian club since replacing Pep Guardiola in 2016, marking his first season in charge with Bundesliga success, but he fell short in both the Champions League and German Cup.
ESPN reports that, despite strong links to the Far East, the experienced manager intends to return to English football before retiring.
Julian Nagelsmann, whose Hoffenheim team earned a 2-0 win over Bayern last weekend, is the current frontrunner to take over from Ancelotti.