Looks like it might happen. Says ESPN:
N:
If the Braves don’t sign Griffey, they could turn to veteran Garret Anderson as a fallback. But sources said that Griffey is Atlanta’s prime target, and the Braves are “in the mix” for his services.The interest is apparently mutual. Griffey lives in Orlando, Fla., where Atlanta’s spring training site is located, and has a good relationship with Braves manager Bobby Cox.
Apparently he’d share time with Matt Diaz in left. While I’m not sure how I feel about the possible move yet, it certainly is an interesting move, and one that seemingly came out of left field nowhere.