With players are DFA'd, there's a 10-day period where the player can either be traded (and it's August, so Kubel would need to clear waivers or be traded to the claiming team), accept a minor-league assignment or be granted outright release and hit free agency.
Kubel, 31, is hitting .220/.288/.324 with five homers and 32 RBI this season in 89 games. He had 30 homers, 30 doubles and 90 RBI last season, but has tumbled down the depth chart behind Gerardo Parra, Adam Eaton and A.J. Pollock as options at the corner outfield spots, not to mention the availability of Martin Prado in the outfield.
Kubel isn't really cut out to be an everyday outfielder, even if he's hitting like he did last year, and would instead be better served as a designated hitter. He's set to be a free agent after the season, so he could be an incredibly cheap option for an AL team hoping for left-handed power from the DH spot.