I think you'll see the Braves or Orioles part with somebody that people wouldn't want to give up.
Remember it took Lino+ to get Thome.
The Greinke market will be diluted some but there are a bunch of mid-market competitive teams that could raise the price.
Greinke on the market will certainly hurt the Cubs with Garza and Dempster.
Garza is considered to be more valuable than Greinke because he's under team control for an extra year beyond this one.
I'm also not so sure there are going to be a ton of teams that will artificially inflate Greinke's value as a trade commodity for the Brewers.
Any team in the NY or BOS area will not be going after him because of possible transition issues to those markets. Same could be said for any L.A. based team/market.
How many teams in mid-sized markets are left that could make a legitimate offer for Greinke?
By my count there are four:
Braves
Cardinals
Indians
Orioles
I really doubt the Brewers would trade Greinke to the Cardinals. Let's take them out for the sake of this example.
The Braves are probably the next strongest suitor for Greinke behind the Orioles. As far as the Indians are concerned, I doubt they pull something off for Greinke - not based on anything I've read or heard, just a hunch.
That (hypothetically) leaves the Braves and Orioles to figure out who wants to offer the strongest package and also pay the money it'll take to keep him there beyond this season. The Braves aren't going to pay Greinke the contract he's going to want/command - Duquette has already gone on record and said that ownership has given him the go-ahead to add payroll this year and beyond.
I'm thinking advantage O's if we really do want him.