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And the German champions have brought Sven Ulreich back to the club on a free transfer in order to fill the newly created vacancy behind first choice Manuel Neuer.
Nubel, who signed from Schalke in June 2020, took on that role last term and ultimately made just four appearances across all competitions.
The 24-year-old is considered a long-term successor to Neuer but had made clear to Bayern his desire to play more regularly next season.
As sporting director Hasan Salihamidzic explained: "It was Alexander Nubel's wish to gain match practice. We supported that."
Nubel joins Monaco on a two-year deal with Bayern reserving the right to recall the player at the end of the coming season.
Of his move, the German said: "I'm pleased to be taking the next step in my development at Monaco.
"It's important to play at a high level, and now I've got that chance at Monaco. I'd like to thank the officials at Bayern Munich for this opportunity. My big goal is to repay their trust in the future."
Ulreich returns as a free agent after his contract with Hamburg, where he spent just one season, was terminated by mutual agreement.
Prior to joining the 2.Bundesliga club, the 32-year-old spent five years with Bayern Munich, whom he signed for from Stuttgart.
Salihamidzic said of the goalkeeper's return: "The condition was that we could sign a serious back-up.
"Our goalkeeping coach Toni Tapalovic advised us about Sven Ulreich, and we're pleased we could reach an agreement with Sven.
"This combined situation is very appealing. It helps everyone involved and fits within our financial framework because Sven returns on a free.
"FC Bayern continues to plan for the future with Alexander Nubel."