"Landon has a verbal agreement with MLS to play in Europe for 2 1/2 months, like Beckham's," Bayern Coach Juergen Klinsmann said on the club's website.
"It's a fantastic situation for me," Klinsmann said. "It gives me the chance to start the second half of the season with four strikers."
Donovan would join Bayern's winter training camp on Jan. 2.
"He's unbelievably quick, and always looks to take on his man," Klinsmann said. "He's a completely different type of striker to the ones we already have. He's a proven top player now and a big name in the American game with more than 100 caps."
Klinsmann said he hoped the talks with MLS "will come to a positive conclusion" and that Donovan would be available to Bayern. "Then it will be up to him to show us what he can do from January onwards."
Donovan is expected to be back with the Galaxy next week as it continues training for its Dec. 6 match against an Oceania all-star team in Auckland, New Zealand. David Beckham will also take part in that game before joining AC Milan later in the month.