"After he presented himself very well, we've agreed to talk to the MLS about a loan from Jan. 1," Bayern coach Juergen Klinsmann said Thursday on the club's Web site.
Klinsmann said Donovan had been given a verbal promise that he could play 2½ months in Europe, during the MLS break, like Beckham in Milan.
"The goal is of course to see if we could rely on him longer, at least until the end of the season," Klinsmann said.
Donovan can play as a forward or midfielder. He led the league with 20 goals in 25 games for the Galaxy this season, has just been voted American football's Player of the Year for a record fifth time and is the U.S. national team's all-time leading scorer.
"It would be a great situation for me. I would be able to go into the second half of the season with four strikers," Klinsmann said.
Klinsmann has been starting Luca Toni and Miroslav Klose as strikers, with Lukas Podolski grumbling about sitting on the bench.
"He (Donovan) is an incredibly fast player," Klinsmann said. "He is a completely different type of forward from the ones we have here."
The coach said Donovan left a very good impression during the 10-day practice stint.
"What we thought is to have him with us at the start of our winter training camp on Jan. 2," Klinsmann said.
Donovan scored both goals for Bayern's first team in a practice game against the reserves Wednesday.
If he comes to Bayern, it will be Donovan's third attempt to break through in the Bundesliga. His previous two attempts, both with Bayer Leverkusen, were failures.