The right-hander opted out of his contract with the Dodgers on Wednesday, foregoing the final three years and $71 million left on his deal. There's no doubt Greinke will command a larger commitment following a season in which he led the Majors with a 1.66 ERA, the lowest by a pitcher since Greg Maddux's 1.63 in 1995.
Greinke, who turned 32 on Oct. 21, may not score as long of a deal as some of the other top starting pitchers on the market, such as David Price, who turned 30 in August. Still, Greinke will require a high annual salary, and he figures to strongly prefer a club that is set up to win.
Which potential suitors could meet those criteria and add Greinke to their 2016 rotation? Here's a look at the top contenders.
Los Angeles Dodgers
Why it might happen: The Dodgers might have the most significant financial resources of any franchise, so cost should not be an issue if they are motivated to retain Greinke. And they have reason to be motivated after the dynamic duo of Greinke and Clayton Kershaw helped lead the club to three straight division titles. With Brett Anderson also a free agent and Hyun-Jin Ryu (shoulder surgery) and Brandon McCarthy (Tommy John surgery) trying to return, the Dodgers badly need starting pitchers they can count on beyond Kershaw.
Why it might not: Just because the Dodgers have the money, it doesn't necessarily mean they will spend it, as president of baseball operations Andrew Friedman and his front office try to build a more sustainable model powered by player development. In the past year, the club didn't end up signing Jon Lester as a free agent or deal for an ace such as Price at the non-waiver Trade Deadline, instead bringing in lower-cost arms in Anderson, McCarthy and Alex Wood.
San Francisco Giants
Why it might happen: Snatching one of baseball's best pitchers away from their division rival would be an impressive way for the Giants to begin another even-year World Series championship run (San Francisco won titles in 2010, '12 and '14). Like the Dodgers, the Giants have a clear ace (Madison Bumgarner) and question marks behind him in the rotation. The winning culture established in San Francisco would be attractive to anyone, and the club made a serious run at Lester last offseason.
Why it might not: The Giants haven't won three championships in the last six years by shelling out big money for free agents, and the last time they did reel in a high-priced arm (Barry Zito), the results weren't great. Would they really be willing to outbid other big-market clubs?
Boston Red Sox
Why it might happen: Last season, Boston's starting rotation ranked 24th in the Majors in ERA (4.39), and of the three pitchers who made more than 21 starts for the Red Sox, none posted an ERA under 4.46. While the Sox have some depth, they need an ace-caliber pitcher, and Greinke obviously would fit the bill. Money isn't usually a major issue for the club, and new club president Dave Dombrowski has a reputation for being aggressive.
Why it might not: Last offseason, the Red Sox spent big on Hanley Ramirez and Pablo Sandoval, and neither acquisition looks too good a year later. Will that create any hesitation? It's also worth noting that Greinke enjoys hitting and may prefer to stay in the National League. That probably wouldn't prevent a deal if the Sox make the best offer, but it could tip the scales slightly in a close race.
New York Yankees
Why it might happen: They're the Yankees, and that means they're always going to be connected to the biggest names on the market due to their resources and history of signing major free agents. They also were only 10th in the American League in starters' ERA (4.25) last season, so a top-of-the-rotation pitcher certainly could make a significant impact here.
Why it might not: Does the team's current reality actually match its reputation for free spending? With more than $180 million in payroll already committed to 10 players for 2016, before dealing with raises through arbitration, the Yanks might turn to less expensive pitching options. They also could allocate the bulk of their resources toward addressing other needs, such as a second baseman. This is also another place where Greinke wouldn't have the opportunity to bat regularly.
St. Louis Cardinals
Why it might happen: Though they might qualify as more of a dark-horse candidate, the Cardinals did show interest in Lester last offseason. They also went on to lead the Majors in ERA (2.94), but the rotation looked worn out against the Cubs in the NL Division Series, and dependable veteran John Lackey is a free agent. With the Cubs and Pirates nipping at their heels in a tough division, perhaps the Cards look to strike a big blow by strengthening a strength.
Why it might not: As mentioned, the rotation is certainly not an area of desperate need, with Adam Wainwright back from injury to join a group that also includes Carlos Martinez, Lance Lynn, Michael Wacha and Jaime Garcia, whose 2016 club option was picked up. Indeed, offense seems like the bigger offseason priority, and the Cardinals could focus their resources on retaining free-agent outfielder Jason Heyward. That would better fit the style of a franchise that typically hasn't spent big on outside free agents.
What would a major free-agent hunt be without the appearance of a "mystery team" or two? There aren't many other obvious candidates who would pay up for Greinke right now, but surprises happen. Look no further than the Nationals swooping in to grab Max Scherzer last offseason despite a starting rotation that already was considered to be among baseball's best.
So who else might enter the fray for Greinke? The Cubs already spent big on Lester a year ago, but they are clear 2016 World Series contenders, with plenty of money. The Tigers are coming off a last-place finish in the AL Central, but they remain in win-now mode and haven't been shy when it comes to increasing payroll. The Angels are a former employer (2012) who are looking to contend, and they have been known to make a splash.
Andrew Simon is a reporter for MLB.com. Follow him on Twitter @AndrewSimonMLB. This story was not subject to the approval of Major League Baseball or its clubs.