Another change in the dugout at the Allianz Arena is being mooted as Niko Kovac struggles to convince in his first season at the helm.
With his side having slipped behind Borussia Dortmund again at home since suffering a setback in Europe, more questions are being asked of the Croat.
It has been suggested that Mourinho could be approached were a fresh start to be made by Bayern this summer, with the Portuguese a proven winner at the very highest level.
Asked at the NTF Coaches Forum in his homeland if he could be tempted by a Bundesliga challenge, Mourinho said in Record: “It's a country I've never trained in. Why not? Let's see.”
The opportunity to work in a new country would appeal to the 56-year-old.
Bayern would fit the bill as a club well placed to compete for more major honours in the future.
Mourinho added on his future plans: “I would like to try and win a third Champions League with a third club and to win a fifth league in a different country.
“But I do not always get what I want and my ambitions are not restricted to this.”
Mourinho has previously admitted that he could be talked into taking the reins at a leading side in France.
He has told beIN Sports: “I can imagine myself as a coach in Ligue 1.
“I am a man who has worked in four different countries, I like to know and learn other cultures. Working in a new championship would be a fantastic experience.”
That message has now been reiterated, but with an invite sent in the direction of Munich should Bayern wish to seek out his services any time soon.