With Alex Gonzalez out for the season, the Brewers need a shortstop. Cesar Izturis can't hit and Edwin Maysonet is a Triple-A veteran who was hitting .214 at Nashville. Ryan is one of the best glove guys in the business; since 2009, he leads all fielders in Defensive Runs Saved. Even if you're not a big believer in defensive metrics, there is solid evidence that Ryan is a top-level shortstop.
Ryan is off to a slow start with the bat, but he's been better in recent seasons than Izturis. The Brewers improve their defense and don't lose anything at the plate.
With Jonathan Lucroy, backup catcher Kottaras is a luxury the Brewers could deal. Yes, the Mariners already have Jesus Montero, John Jaso and the currently disabled Miguel Olivo, but Montero will still spend a lot of time at DH and Olivo isn't any good. Kottaras does have a similar skill set to Jaso (left-handed hitter), but is maybe a little better. With Mat Gamel also injured, the Brewers may give Green playing time at first base or third base (with Aramis Ramirez moving to first), but if they're more committed to Travis Ishikawa, Green may be expendable. The Mariners get another first base/third base guy to throw into the Justin Smoak (starting to look like he can't hit)/Alex Liddi (we'll see if he can hit)/Chone Figgins (we know he can't hit)/Kyle Seager corner mix. Seager is probably stretched defensively at shortstop, but he can move over for now, at least until prospect Nick Franklin is ready in a couple years. The Mariners also have Japanese veteran Munenori Kawasaki who can play there.
You could actually argue that those two players aren't worth Ryan, who has accumulated 9.5 Baseball-Reference WAR since 2009. Kottaras is a solid backup while Green grades as a marginal corner guy. If you're looking at prospects, the Milwaukee system is pretty thin. You'd be looking at one of their Class A pitching prospects -- Taylor Jungmann or Jed Bradley -- but the Brewers would be unlikely to trade one of those two.
Still, seems like a potential match here. Ryan is an underrated asset, but exactly the kind of player the Mariners should be looking to flip if they can find a team which values his defense.