The 72-year-old Heynckes led Bayern to the domestic league and Cup double and the Champions League title in 2013 but then had to make way for Spaniard Pep Guardiola.
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According to the Bild newspaper Heynckes, who also led Real Madrid to the Champions League title and coached Benfica, Athletic Bilbao and a string of Bundesliga clubs, will take over until the end of the season.
The club could not be immediately reached for a comment.
Italian Ancelotti took over last season but was fired last week after the German champions slipped to second place in the league after twice squandering a two-goal lead in consecutive games.
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They had also been beaten 3-0 at Paris St Germain in the Champions League.
Heynckes, who has not worked since 2013, had also coached Bayern from 1987-91 and briefly took over at the end of the 2008-9 season before becoming head coach between 2011-13.
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