It's unlikely, of course, even for a loan. He did practice with Arsenal last year to get in shape. Obviously, Becks wants to stay in as high a form as possible to continue playing for England.
I don't think Beck's contract allows for a loan to another team. It would be the Galaxy's luck to have him badly injured again. Alexi Lalas used to insist that Becks practicing with another team was fine, playing was another matter. Of course, he said something similar to Amado Guevara way back in the MetroStars era, and Amado played games during the offseason anyway. I'm trying to think of the last player MLS loaned out to any team, and I'm drawing a blank. Was it Brian McBride with his Everton gig in 2002? I think there's a more recent example, but I can't remember it. Suffice it to say, though, MLS does not readily loan players.