Atlanta has identified lefty in the pen as its biggest need, with Oliver Perez, who interested the Braves in the winter, Wesley Wright, Neal Cotts, Tony Sipp and Mike Dunn are among other accomplished pen lefties believed available in trade.
Miller, a free agent after the year, is having a spectucular season in Boston's pen (64 strikeouts and only 12 walks in 39 1/3 innings to go with a 2.52 ERA), and the fading Red Sox have said they are now "listening" to trade inquiries.
The Braves in their pen currently have only one left-hander, Chasen Shreve, who was called up a week ago, in their pen. Shreve replaced Luis Avilan, who was sent down.
The Braves have won more regular-season games than anyone else since 2010, but have perennially adhered to a budget of $90 million to 100 million. Since they've gone "over budget" this year with the $14 million signing of Ervin Santana in spring training following elbow injuries to young starters Kris Medlen and Brandon Beachy, they aren't expected to have room for even bigger moves. But Miller would be a big help.