Greinke is the biggest piece the Brewers have. With the news that the Brewers will only receive one compensation pick if he leaves in free agency (instead of two like the old days), the value of keeping him all season and then letting him leave in free agency lessens greatly. There are a lot of issues tied into dealing him, however.
The first (and biggest) one is that the Brewers offered him a contract extension in the $112 million range. Frankly, he would be a lunatic not to take it. He was offered near-Matt Cain money, and although his upside is higher than Cain's (Cain hasn't come close to Greinke's Cy Young season in '09, which was done in the tougher league and in a tougher run environment), he's nowhere near as safe or consistent year-to-year. He's also unlikely to find a deal like it in free agency; Cole Hamels will command the biggest money, and while Greinke is a clear second there are many solid young-ish arms that will cost a fraction of what Greinke will likely ask for (McCarthy, Liriano, Anibal Sanchez, Edwin Jackson, etc.). Tied in with that is the fact that many high-payroll teams are either disinterested in Greinke or looking to cut costs. The only team that can reasonably be forecasted to offer Greinke a big deal is the Dodgers, and it's no secret the covet Hamels more than anyone.
Another issue is there's plenty of pitching available on the trade market. Why give up a king's ransom for Greinke when you could have Ryan Dempster or Franciso Liraino for less? And if you are willing to go all in, Cole Hamels is the better option and you could argue James Shields is a worthwhile investment as well.
Oh, and about the king's ransom; it's not going to happen. Seeing as the team that trades for Greinke will not receive draft picks when he leaves in FA, the Brewers have much less leverage. They'd either receive a C-level prospect that's close to the bigs but has low upside, or someone with tools who's light years away from contributing. Or a collection of below-average major leaguers. Ick.
Marcum is also a free agent at the end of the year, but he's currently hurt and the only chance the Brewers have of moving him is a post-deadline waiver deal. Not likely to get much for him.
Also a free agent. He has a team option for next year but only an imbecile would not buy him out. He's just about worthless as a trade asset.
See Wolf, Randy.
He's a "closer", and he's a big name, so there's a non-zero chance that a GM become nostalgic and gives up a 4th outfielder or relief prospect for him. The team could move him for nothing just to cut costs.
Axford is cheap and under team control for awhile yet, and that's what would make him tempting to a team desperate for relief help despite his struggles. Seeing as relievers a volatile and Axford is sexy when he's right, he could bring back an interesting return. A progressive-thinking GM would think about moving him, but progressive isn't exactly how I would describe Doug Melvin. Not going anywhere.
Hart could bring back a nice return seeing as the first base position has weakened this year and he's signed through next year on a very reasonable deal. He has a great relationship with the organization and is a good extension candidate, so it's highly unlikely he's dealt.
It's odd to think that Ramirez could bring back the biggest return, but it's probably true. Bats are hard to come by on the trade market, and he's about as reliable as they come. He's also not a rental, but the next two years of his contract are unsightly. The Dodgers are reportedly interested in him and might part with Nate Eovaldi or (hopefully) Zach Lee to get a competent bat. If they don't get Chase Headley, it could happen. Let's hope it does.
He's the offensive version of K-Rod. Having a bad year, but brings value as a part-time player and was tremendous last year. We can only hope teams trade for the 2011 version of Morgan. Would bring little-to-nothing in return, but would open up playing time for prospect Logan Schafer.
George is a great backup catcher and would be an extremely useful piece for a playoff team. It's hard to gauge what return he could bring because his value might greatly exceed how good he actually is. There just aren't many catchers on the market. He's also a decent pinch-hitter but that might be his only role on the Brewers once Jonathan Lucroy returns. Maybe they could package him with Randy Wolf in a trade (GET IT? IT'S A BREWERS JOKE).
Seems like a classic post-waiver deal. Decent pinch-hitter, can play a couple positions.
There's not much else of worth that the Brewers could move, and certainly not for any real value. I suppose Manny Parra and Kam Loe could go, but whether they like it or not the Brewers have to field a bullpen of some kind. No one wants the shortstops. Braun, Aoki, Gallardo, Lucroy, and anyone else young/cheap are safe, as they should be.