Yossi Benayoun has been by no means a star for Chelsea, making just fourteen appearances over three seasons. He made more appearances on loan with Arsenal over the 2011-12 season than he has with Chelsea for the whole of his contract. Thus it's not surprising that he wants out, but it may surprise you that he wants to come to America. Here's his quote, from Chelsea blog We Ain't Got No History.
At the moment I'm in talks with several European teams. I'm checking my options but, to tell you the truth, America is one of my favourite options. I'm trying to do everything I can to come to America and play in the MLS, and hopefully it works out in the next few weeks.
-Source: Sky Sports.
I'm quoted in WAGNH's article as saying Benayoun could be a third DP target for the Galaxy. Distribution has been one of Bruce Arena's main concerns for the club, and if Arena were willing to change formation a bit and have Benayoun play behind Robbie Keane in a 4-4-1-1 good things could come. I also mentioned Los Angeles' Jewish community as being a solid reason for signing the Israeli national team player. I'm all for the LA Galaxy having representatives from as many of the cultural bases in Los Angeles as possible.
The Sky Sports article mentions that the New York Red Bulls have expressed interest in the past, and certainly they'd look to be LA's biggest competition in getting a deal done. I have a source who says Benayoun was offered to MLS last fall and that LA listened, but there were too many questions with David Beckham and Landon Donovan. Other MLS offers for him were deemed too small.
So it's going to be an overbid situation, and the hope is simply to avoid buyers remorse. He didn't net a goal for West Ham while on loan, but LA has had success with another international who was being loaned around in the EPL.