The Dodgers have five outfielders each pushing for a starting job. Yasiel Puig, and Joc Pederson are almost certainly not for trade, but their have been rumors that Ethier, Kemp, and Crawford are all on the block. The issue is these players salaries no one in the majors wants to pay the $62.2 million owed to Crawford, the $53.3 million owed to Ethier, or the $107 million owed to Kemp. The most likely trade of these three is Matt Kemp because he is the most likely of the three to earn his worth. Matt Kemp's rumors have mostly involved the Orioles or Padres including a rumor of Kemp for Padre's Catcher Yasmani Grandal.
The Red Sox have even more outfielders than the Dodgers. Their EIGHT outfielders (as well as Brock Holt who can play just about anything) ready for a starting role are: newly signed Hanley Ramirez, as well as, Rusney Castillo, Shane Vistorino, Jackie Bradley Jr., Daniel Nava, Yoenis Cespedes, Mookie Betts, and Allen Craig. The Red Sox must trade at least two (hopefully three to five) of these players to even have a chance in 2015, but so far their have only been limited rumors for trading anyone but Yoenis Cespedes. The rumors of a Cespedes trade have been with the Tigers, for Rick Porcello, or with the Padres for Ian Kennedy.
The Braves do not have nearly as much of a surplus of outfielders as the Sox and Dodgers, but there have been rumors that offers for both the Upton brothers are being considered, as well as Evan Gattis.