But which one?
Industry sources identify the Los Angeles Angels, Los Angeles Dodgers, Texas Rangers and Washington Nationals as his top suitors. The Kansas City Royals also plan to acquire a rotation leader and wouldn't mind bringing Greinke back for a second tour of duty.
It is possible that he lands with none of the above. Last winter's top free agents—Prince Fielder and Albert Pujols—got paid by clubs who weren't rumored to have interest.
These updated odds recognize that a mystery team could sign the 29-year-old (there's about a three percent chance), while specifying what likelihoods each of the five favorites currently have.
Greinke began his professional career with the Kansas City Royals.
Even with Jeremy Guthrie and Ervin Santana in tow, the Kansas City Royals want to continue adding to their starting rotation.
Obviously, Zack Greinke has a lot of history with the organization.
K.C. made him a first-round draft pick in 2002, called him up to the majors in 2004 and supported him through social anxiety disorder and depression during the 2006 season. Greinke emerged as an elite player in 2008 (13-10, 3.47 ERA, 183 SO in 202.1 IP) and became a fully-fledged ace the next year, running away with the AL Cy Young Award.
But the Royals are extreme longshots to reunite with the right-hander after losing 90 games last summer. Greinke's other suitors all posted winning records, either qualifying for the postseason or at least staying in contention into late September.
Money is another issue. CBS Sports' Jon Heyman doubts Kansas City would offer $150 million, the guaranteed amount Greinke expects to earn in a six-year deal.
Using its surplus of high-ceiling youngsters, the club is more likely to bolster its pitching staff via trade anyway.
Greinke started 13 games for the Los Angeles Angels last season.
The Los Angeles Angels acquired Tommy Hanson on Nov. 30 to fill one of their vacant rotation spots. Following four MLB seasons with the Atlanta Braves, he'll earn about $4 million through arbitration (via Matt Swartz, MLB Trade Rumors).
MLB.com's Alden Gonzalez tweets that Zack Greinke remains "in play" despite the transaction.
Last July, the Angels traded three top prospects to the Milwaukee Brewers to rent Greinke's services down the stretch. He pitched effectively (6-2, 3.53 ERA, 1.19 WHIP in 13 GS), but couldn't elevate them to the playoffs.
Greinke evidently has some interest in re-signing. Mark Saxon of ESPNLosAngeles.com reports that he recently arranged a face-to-face meeting with team executives.
Alas, major league sources tell Danny Knobler of CBS Sports that an agreement is unlikely. Los Angeles plans to spend more on its bullpen after missing out on Kyuji Fujikawa. And regardless, Albert Pujols, Jered Weaver, Vernon Wells and C.J. Wilson have back-loaded deals that dominate the payroll.
Neftali Feliz won't rejoin the Texas Rangers rotation until midseason.
Jon Heyman tweets that the Texas Rangers cannot afford both Zack Greinke and Josh Hamilton.
Wooing the former is believed to be a higher priority with starters Neftali Feliz (Tommy John surgery) and Colby Lewis (torn flexor tendon) both in questionable health. Indeed, T.R. Sullivan of MLB.com writes that Greinke is "at the top of their shopping list."
Texas' recent success serves as a recruiting advantage. Only the San Francisco Giants can claim the same three postseason appearances and two World Series berths since 2010.
Though their home ballpark has a hitter-friendly reputation, Greinke shouldn't be deterred. His career numbers at Rangers Ballpark are outstanding (2-3, 2.83 ERA, 1.04 WHIP in 7 G).
In a Dec. 2 post, Heyman reports that Texas has met with Greinke.
GM Mike Rizzo on Greinke: "What's not to like?"
The Washington Nationals have skyrocketed into Zack Greinke contention. Just days ago, Bleacher Report's Rick Weiner considered them 60-1 longshots.
Who improved their odds? Denard Span.
Washington initially seemed intent on finding their long-term center fielder in free agency. Michael Bourn, Angel Pagan and B.J. Upton all made sense.
Instead, general manager Mike Rizzo moved prospect Alex Meyer to the Minnesota Twins for Span, who is already locked into a team-friendly contract. The trade leaves Rizzo with plenty of money left to spend.
Baseball insider Jon Heyman insists that the team loves Greinke and tried hard to acquire him two winters ago.
Owner Ted Lerner is incredibly wealthy and no stranger to nine-figure guarantees (e.g. Jayson Werth and Ryan Zimmerman). Being in the National League also helps Washington because Greinke enjoys batting (.600 OPS in 2012).
Non-tendering John Lannan and allowing Edwin Jackson to reach free agency makes room for Greinke alongside four excellent starting pitchers. As a competitor, he would be encouraged to see the integral members of last year's 98-win Nationals returning.
Magic Johnson and the Los Angeles Dodgers would win any bidding war.
Without hesitation, the Los Angeles Dodgers would make Zack Greinke the richest pitcher in MLB history (surpassing CC Sabathia's $161 million deal). They spoke to him last Thursday, according to Yahoo!'s Tim Brown, and believe he is "critical" to their future success.
The Dodgers already resemble an All-Star team with elite performers like Adrian Gonzalez, Kenley Jansen, Matt Kemp and Clayton Kershaw. Then there is Josh Beckett, Carl Crawford and Hanley Ramirez, each of whom excelled earlier this decade.
If Greinke enjoyed the city during his Los Angeles Angels stint (and it's believed he did), he should have no objections to signing with the über-talented Dodgers.