The Braves are interested in trading for Jackie Bradley Jr. according to Peter Gammons, who says that the Red Sox might be willing to pull the trigger on a trade once the team is certain of their outfield's health heading into the season:
When the Red Sox know the health and the predictable production of all their outfielders this spring, they may well make a trade or two; the Braves have called and made it clear they have strong interest in Jackie Bradley, but that is a post St. Patrick's Day discussion.
As it stands, Bradley is well down the depth chart in the outfield for the Red Sox. Hanley Ramirez, Mookie Betts, and Rusney Castillo are the expected starters before spring training, with Shane Victorino providing backup in the more difficult defensive positions and Daniel Nava/Allen Craig likely taking over as needed in left (and smaller right fields than Fenway's) depending on matchups. That leaves Bradley as mostly a late-game defensive replacement if everyone else is healthy.
The Red Sox might be reluctant to trade Bradley away when his value is so low. If he's capable of hitting even just a little, Bradley's glove would make him quite valuable indeed. A decent run through spring training could help (and Bradley is obviously capable of at least that), but there's no substitute for regular season at bats, and those are in short supply. The team will have to make a tough choice or two before rosters finalize, assuming nobody starts off on the disabled list, and having a team that isn't just interested, but actively pursuing one of their surplus outfielders could make things easy for the Sox.