The Bavarians are three points off the pace in the Bundesliga and are now on the hunt for a new boss.
Ancelotti was summoned for crisis talks back in Germany today after the loss in which Edinson Cavani, Dani Alves and Neymar scored for the French giants.
A press conference has been called for this afternoon to officially announce Bayern’s decision.
Bayern chief Karl-Heinz Rummenigge called for “consequences” following the Bundeliga giants’ worst group stage defeat in the Champions League for 21 years.
Speaking at the club’s traditional post-match banquet at the team hotel, he said: “What we saw today was not FC Bayern, I think we can all agree that.”One report in Germany today claimed the former Chelsea boss is set to be replaced by his assistant Willy Sagnol or former Borussia Dortmund coach Thomas Tuchel.
Ancelotti, who has a contract till June 2019, has also been linked with a return to his former club Milan.
The Italian was already under increasing pressure with the Bavarian giants only third in the Bundesliga after a sluggish start. They drew 2-2 at home to Wolfsburg last Friday after leading 2-0.
But Ancelotti, who was sacked by Chelsea in 2011, made six changes for the trip to the Parc des Princes and saw his side destroyed 3-0.
“It was a bitter defeat,” Rummenigge said. “One we must talk about. One we must analyse. And one from which we have to draw our consequences.
“It’s important we get our act together soon and show we are Bayern Munich, a team which has made a great stir in Europe and Germany in recent years.”
Ancelotti’s relaxed management style has come in for criticism in the German press obsessed by events at FC Hollywood.
He succeeded Pep Guardiola last year with the task of overseeing a transiton from the treble winning team of 2013 and bring through the next generation like Kingsley Coman and James Rodriguez.
Franck Ribery, 34, and Arjen Robben, 33, were on the bench in Paris.
Asked if the team supports Ancelotti, the Dutchman said: “I will not answer that question. It was a painful defeat.”
By contrast, Paris Saint-Germain announced themselves as serious Champions League contenders with the win. The French side lost 6-1 to Barcelona last season but have since recruited Neymar and Kylian Mbappe.
Thiago Silva said: “It was a huge win against a big team and also a great coach (Carlo Ancelotti). I believe that PSG has shown its true face. I think we deserved this win. The future looks good.”