The great free-agent shortstop class of 2021-22 is set to keep the Hot Stove burning next winter, but now that Fernando Tatis Jr. has firmly established the market for top shortstops with his 14-year, $340 million deal, could we see more players agree to extensions in the near future?

Here’s a look at eight candidates (listed alphabetically) for the next big extension -- and four others who are unlikely to get such a deal done:

Javier Báez, SS, Cubs, age 28
Eligible for free agency after the 2021 season

Kris Bryant and Anthony Rizzo are also slated to become free agents next offseason, but Báez feels like the logical candidate to be extended in Chicago. Following two strong seasons in 2018-19, the 28-year-old struggled at the plate in '20, though he did win his first career Gold Glove Award. President of baseball operations Jed Hoyer said he plans to sit down with all three players this spring, though it remains to be seen if anything comes of those talks.

Cody Bellinger, 1B/OF, Dodgers, age 25
Eligible for free agency after the 2023 season

Corey Seager, SS, Dodgers, age 26
Eligible for free agency after the 2021 season

The Dodgers are clearly open to big extensions, having given Mookie Betts a 12-year, $365 million deal a year ahead of free agency. Seager is part of next year’s shortstop free-agent mega-class, while Bellinger remains arbitration-eligible for two more years. Both players are represented by Scott Boras, who tends to prefer taking his players to free agency. There have been exceptions -- Stephen Strasburg signed an extension with the Nationals in 2016 -- and either of these two players could become the next.

Michael Conforto, OF, Mets, age 27
Eligible for free agency after the 2021 season

Conforto won’t get the same attention publicly as new teammate Francisco Lindor, but make no mistake, the Mets see the outfielder as a big part of their future. Conforto had his best offensive season in 2020 (albeit in a shortened campaign), and while he doesn’t have a lengthy track record to match George Springer, he’s three years younger, making Springer’s six-year, $150 million contract a likely starting point.

Rafael Devers, 3B, Red Sox, age 24
Eligible for free agency after the 2023 season

With two more arbitration-eligible years, there isn’t a huge rush for the Red Sox to get something done with Devers. But Chris Sale and Xander Bogaerts are the only players with guaranteed money on the books beyond 2022, when J.D. Martinez, Nathan Eovaldi and Enrique Hernández all hit free agency, clearing more than $44 million from the payroll. Devers has become a very productive bat in Boston’s lineup and should be its next target for a lengthy contract.

Francisco Lindor, SS, Mets, age 27
Eligible for free agency after the 2021 season

From the moment the Mets traded for the All-Star shortstop, it seemed like a matter of when -- not if -- New York would extend its new superstar to a deal likely to exceed $300 million. Lindor is open to an extension, but he's said he doesn’t want to negotiate during the season. That gives the Mets about six weeks to get it done, and given Steve Cohen’s deep pockets and desire to win, you’d have to assume they’ll make it happen.

Gleyber Torres, SS, Yankees, age 24
Eligible for free agency after the 2024 season

For years, the Yankees veered away from extensions, allowing their players to go through their arbitration years and reach free agency rather than locking them up any earlier than they had to. That has changed recently, with Aaron Hicks and Luis Severino signing extensions in 2019. Torres is arbitration-eligible for three more years, but the Yankees could try to buy out those years (and more?) in exchange for cost certainty. Signing Torres would also squash any speculation about the Yankees’ plans to pursue one of the big free-agent shortstops next offseason.

Trea Turner, SS, Nationals, age 27
Eligible for free agency after the 2022 season

At some point, the Nationals will do what it takes to extend one of their offensive stars, right? Having let both Bryce Harper and Anthony Rendon walk away as free agents in recent years, the next two candidates are Turner and Juan Soto (more on him later). Turner isn’t set to become a free agent until the end of the 2022 season, at which point the other star shortstops around the league will all have signed big contracts. Washington could try to jump the market and get Turner signed before the price tag for a star at his position continues to rise even further.

Players unlikely to sign extensions

Carlos Correa, SS, Astros, age 26
Eligible for free agency after the 2021 season

Houston was unable to extend George Springer, who signed with the Blue Jays as a free agent this winter. Will the same fate await Correa, who is slated to hit the open market next fall? Correa finally stayed healthy during the shortened 2020 season, but his numbers declined. Unless Correa -- who recently said he wants to be “an Astro for life” -- has his heart set on staying in Houston even if it costs him some money, it might make sense for both sides to let the 2021 season play out before committing to a long-term deal. The Astros also have Justin Verlander, Zack Greinke and Lance McCullers Jr. headed to free agency next offseason, leaving GM James Click with a lot of work to do in the coming year.

Aaron Judge, OF, Yankees, age 28
Eligible for free agency after the 2022 season

Unlike many of the game’s young stars, Judge’s age might work against him; he’ll be entering his age-31 season when he first hits free agency. Judge’s impact on the Yankees’ lineup isn’t in question, but his ability to stay healthy is an issue. If the Yankees decide to extend one player, Torres seems like a better bet than Judge for both his age and durability.

Juan Soto, OF, Nationals, age 22
Eligible for free agency after the 2024 season

Soto is widely considered the best pure hitter in the game, so it would make sense for the Nationals to do whatever it takes to keep him in Washington for a long time. But with three more arbitration-eligible years before he becomes a free agent, Soto could set arbitration salary records if he continues to produce at his epic levels. Boras might view Soto as the only player who could approach (or pass?) Mike Trout’s record $426.5 million deal, so locking him up before he has a chance to test the market feels unlikely.

Trevor Story, SS, Rockies, age 28
Eligible for free agency after the 2021 season

When the Rockies traded Nolan Arenado to the Cardinals, many believed that Colorado would then lock up Story to a long-term extension. But it takes two to tango, and after seeing Arenado get traded less than two years after signing his $260 million extension, why would Story tie himself to the Rockies rather than testing the open market after this season?