"Justin Bieber's management contacted us and they will give up Mally," a Munich animal welfare organization spokeswoman told E! News.
"They are asking us for a good home for Mally," Roberta Mioni Coltro of the Munich Tierschutzverein said, adding authorities still needed official confirmation from Bieber manager Scooter Braun, rather than just an email.
But Mally's ultimate home will be decided by the German government's Federal Agency for Nature Conservation, not the animal welfare group, Coltro said.
"We only can make a recommendation and we don´t want to send Mally in the zoo, because the zoos will only [publicize] Mally," she said.
"We want Mally in a rescue center or some organization for primates," Coltro said.
The 17-week-old capuchin monkey, native to Central and South America, was confiscated by German authorities March 28 after Bieber, who arrived in Munich on a private plane, could not produce the proper paperwork to bring the animal into the country, E! said.
The animal -- which can grow to 22 inches and has a tail as long as its body -- was reported by BuzzFeed to be a 19th-birthday gift for Bieber from music producer Jamal "Mally Mall" Rashid, who has a capuchin of his own, named Bubbz.
Bieber had his birthday March 1 while his "Believe" tour promoting his studio album of the same name was in London, but he picked up the monkey during a brief visit home to Los Angeles, Buzzfeed said.
Bieber is completing a three-day stop in Sweden and continues to Finland, Russia and Turkey, before going to the United Arab Emirates and South Africa and returning to the United States.
Bieber gave away his hamster Pac to a fan at an Atlanta concert in December. Pac died last month.