Ancelotti led Bayern to a fifth consecutive Bundesliga title last season in his first campaign in charge after succeeding Pep Guardiola at the Allianz Arena.
However, the Bavarians lost to Real Madrid in the quarter-finals of the Champions League and to Dortmund in the semi-finals of the German Cup.
Ancelotti has also coached Parma, Juventus, AC Milan, Chelsea, PSG and Real Madrid, winning the Champions League three times in his career.
Among the potential replacements being mentioned is Thomas Tuchel, currently a free agent after leaving Dortmund at the end of last season.
Factfile on Carlo Ancelotti, who was sacked as coach of Bayern Munich on Thursday:
Name: Carlo Ancelotti
Nationality: Italian
Age: 58 (born June 10, 1959)
Place of birth: Reggiolo, Italy
Playing career
Clubs: Parma (1976-79), Roma (1979-87), AC Milan (1987-1992)
National career: Italy (26 caps/1 goal)
Honours: European Cup (1989, 1990), Intercontinental Cup (1989), UEFA Super Cup (1990), Italian Serie A (1983, 1988, 1992), Coppa Italia (1980, 1981, 1984, 1986)
Coaching career
Clubs: Reggiana (1995-96), Parma (1996-98), Juventus (1999-2001), AC Milan (2001-09), Chelsea (2009-2011), Paris Saint-Germain (2011-13), Real Madrid (2013-2015), Bayern Munich (2016-17)
Honours: Champions League (2003, 2007, 2014), FIFA Club World Cup (2007, 2014), UEFA Super Cup (2003, 2007, 2014), Italian Serie A (2004), English Premier League (2010), French Ligue 1 (2013), German Bundesliga (2017), Coppa Italia (2003), FA Cup (2010), Copa del Rey (2014), Italian Super Cup (2004), Community Shield (2009), German Super Cup (2016, 2017)