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.
According to the Bild newspaper, Heynckes - who also led Real Madrid to Champions League glory and coached Benfica, Athletic Bilbao and a string of Bundesliga clubs - has come out of retirement to take over until the end of the season.
The club is yet to 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.
They also lost 3-0 at Paris St Germain in the Champions League.
Heynckes, who has not worked since 2013, had also coached Bayern from 1987-91. He briefly took over at the end of the 2008/9 season before becoming head coach from 2011-13.