The 26-year-old Nubel, whose contract with Bayern runs to 2025, had been a main candidate to come in until the end of the season after Germany keeper Neuer broke his leg during a skiing holiday last month.
Neuer has been ruled out for months and will miss the rest of the season following surgery.
"The transfer is off the table," Nuebel's agent Stefan Backs told broadcaster Sky late on Monday. "Alexander will play the second half of the season at Monaco."
Neubel later posted on social media a photo of himself in a Monaco outfit during a break in training with the line "What else?".
Bayern have been desperately searching for a replacement for Neuer with the team top of the Bundesliga ahead of the season restart against RB Leipzig on Friday.
The Bavarians, who are four points clear at the top of the Bundesliga and six ahead of third-placed Leipzig, are also facing Paris St Germain in the Champions League Round of 16 next month.
Their only experienced keeper is 34-year-old Sven Ulreich, with the others, including 20-year-old Johannes Schenk, having no first team experience.
