The White Sox seem to be our most compatible trade partner right now for several reasons:
1) Ned Colletti has shown a propensity to do deals with Kenny Williams. In fact, the White Sox have been our most frequent trade partner since Ned's arrival, and I think the Juan Pierre trade showed a willingness on both sides to work together and get something done.
2) Kenny Williams has a propensity to trade for guys with potential, even if they are overpaid and haven't quite lived up to that potential. Alex Rios would be one example and guys like Loney and Broxton fit this description.
3) The White Sox may be in need of both a Closer and a first baseman. Conveniently, the Dodgers have one of each in Loney and Broxton.
4) The Dodgers could potentially use an Outfielder, a 3B and a 2B. The White Sox are reportedly willing to entertain offers for Carlos Quentin and Gordon Beckham. Also, at 3B, they have a logjam with Mark Teahen, and two of the best 3B prospects in the game in Dayan Viciedo and Brent Morel.
I doubt there is a deal that would get done as simple as a 1 for 1 or 2 for 2 swap. Maybe some prospects and/or money would have to be involved. However, the needs and availability are there on both sides to get something done that would be beneficial to both teams.