Ancelotti's sack was triggered by 3-0 loss to Paris Saint Germain at the Pac de Princes on Wednesday.
Former AC Milan, Chelsea and Real Madrid manager Ancelotti was in charge at the Allianz Arena for 15 months since taking over from Pep Guardiola in July 2016.
Potential full-time candidates for the Bayern job include Hoffenheim coach Julian Nagelsmann, who handed Ancelotti a 2-0 defeat earlier this season, or current assistant manager Willy Sagnol, a former French worldwide who played for the Munich club.
Germany has a lot of fine young coaches - 30-year-old Julian Nagelsmann from Hoffenheim is the name most often mentioned, though Thomas Tuchel, 44, is free after departing Dortmund - but whoever replaces Ancelotti will inherit an aging team in need of replacements.
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The Italian had come under pressure in the early stages of the new campaign after a 2-0 defeat to Hoffenheim in September.
Bayern CEO Karl-Heinz Rummenigge warned there would be consequences following the defeat in France, with SportBild reporting on Thursday morning that a meeting was due to be held later in the day to discuss Ancelotti's future.
"The one we saw in Paris is not the real Bayern Munich, we all agree. I expect the team to produce a positive response and show absolute determination to achieve our targets for the season". "Our team's performances since the start of the season have not met our expectations", said Rummenigge. Then there is nothing to misunderstand or to interpret wrong. I think it's important to turn things around after this loss, to present as Bayern Munich and to show we are a team, [the one] which performed well in Europe and in Germany a year ago. In the first half, we had good control of the game, good possession, some chances. "That's where we have to continue".