If you sprechen sie Deutsch, then you can take a look here and see that it says Edson Buddle and FC Ingolstadt 04 have parted ways. This means that Buddle is now a free man, and able to sign with MLS any time between now and April 15. Other federations have different dates for the end of their free transfer window, and it is possible Buddle could end up in England; for example.
Assuming for a moment he is coming back to MLS, there has been some discussion on twitter as to how his return would be handled. His return would be subject to two sections of the MLS Roster Rules: Player Acquisition Mechanisms and Right of First Refusal.
The first thing to keep in mind, is that MLS is a single entity in the eyes of the international community, so from FIFA's end the only important part is that Buddle re-signs with MLS. Most are familiar with the rule regarding MLS players who have gone abroad and have appearances with the US National team, thanks to Kenny Cooper, Fredy Adu and the like. However, that rule only applies when his previous MLS club sold his contract overseas.
Less known is how right of first refusal works. Because Edson Buddle was out of contract, and LA gave him a bonafide offer, they retain right of first refusal on his return. If a team receives allocation money as a result of a transfer, they do not retain right of first refusal.
Now remember, these are all internal MLS rules. Think of it this way. Within MLS, it's decided that if you really wanted someone and they got away, you get to welcome them back. If you didn't, then they'll be given to the neediest team. To put it another way, if they break up with you, you can take them back. If you break up with them, they're gonna find someone who cares about their needs.
So, should MLS sign Edson Buddle, the Galaxy would be allowed first crack at him. They can trade that right to someone else, sign him and then move him, really the possibilities are endless. But, because Buddle broke up with Bruce Arena, everything has to go through him.