This will occur roughly four weeks after breaking his collarbone in a benches-clearing brawl with Carlos Quentin, which is certainly better than even the most-optimistic Dodgers fan could have rooted for. Greinke has said that he will be on a limited pitch count, and that it will take him some time to build his stamina back up.
When Don Mattingly was asked about the situation, he essentially didn't answer it at all, which means that he is probably under strict instruction from higher up the food chain not to talk about the topic.
The article states that Greinke has already thrown three bullpen sessions, and is touching 90 mph with his fastball. He is still working to get his stamina back to an acceptable point, but it appears as though he has reached the point where the team feels as though he is ready to pitch in game action.
For a reeling Dodgers team, this is a nice bit of news that cold potentially inspire them to turn the season around. If they can start playing well, and then see the return of Greinke, they could ride the momentum right back into the playoff-picture.