NASHVILLE, Tenn. — Chris Getz made it known in his introductory press conference: There are no untouchables on this White Sox roster as he embarks on a dramatic makeover of the organization.

That would, however surprisingly, include Luis Robert Jr.

But how realistic is it that the White Sox would actually move Robert? After all, their center fielder ranks as one of baseball’s best, fresh off an MVP-type season that saw him win a Silver Slugger. He’s under club control for four more years on a contract that makes him relatively affordable, considering the production.

The White Sox wouldn’t really trade him, would they?

No, it turns out, probably not.

“Luis Robert is a very difficult player to move and expect that your club is going to get better because of it,” Getz said Monday at the Winter Meetings in Tennessee. “That being said, there might be a club out there that is willing to offer something that you feel can help you immediately and in the long term.

“But we’re talking about one of the best players in baseball, and we’re very fortunate to have him with the Chicago White Sox. So I have a tough time seeing him wearing another uniform next year.”

That might not put the idea of the White Sox shipping Robert out of town completely to bed, as there might be a team tantalized enough by the prospect of him in the middle of its lineup that it makes Getz an offer he can’t refuse.

But it’s as close to “untouchable” as any one of Getz’s players is going to get this winter.

Meanwhile, though, it looks more and more likely that Dylan Cease will be wearing another uniform in 2024, given the amount of trade buzz here in Nashville surrounding an arm who might just be the best on the market, alongside free agents Yoshinobu Yamamoto and Blake Snell.

As the Winter Meetings started Monday morning, Cease’s trade market reportedly included a host of teams, including the Dodgers, Braves, Giants, Orioles, Reds and Cardinals. With two years left of club control and only one year removed from a second-place finish in the Cy Young vote, Cease figures to be attractive to anyone in the market for pitching. Which, you know, is usually everyone.

But reports that Getz might be waiting to see where Yamamoto and Snell land before pulling the trigger on a Cease trade were reinforced when the general manager spoke Monday and he expressed no desire to make a move anytime soon.

“There’s certainly no urgency to move Dylan Cease,” Getz said. “Like I’ve said from the beginning, if there’s an opportunity to help our club both near term and long term, we’ll look at it. But we’re talking about one of the best pitchers in baseball.

“There’s a responsibility for your organization, for the Chicago White Sox, to do what’s best for them. But Dylan’s a star in our game. There’s no real reason to come here and expect us to move a Dylan Cease, but if a team brings something that meets a threshold that we feel we’ve just gotten a lot better, then we’re going to do that.”

Getz said Monday evening that his White Sox front office wasn’t close to finalizing anything, let alone a trade for one of the game’s top pitchers, and it might be a slow Winter Meetings for the South Siders, as it has been for most of baseball as the game waits for Shohei Ohtani to break the market open.

The White Sox aren’t swimming in the Ohtani waters — chairman Jerry Reinsdorf took his team out of that sweepstakes in August — but they might be forced to wait for the game’s best player, too.

That appears to be just fine for Getz, though, who’s right to suggest that there’s no need to trade Cease as soon as possible. He’s under control for two more seasons and would figure to fetch a nice price at the trade deadline, should he stay with the White Sox.

But as Getz plots his reimagining of baseball at 35th and Shields, his best shot to infuse some depth and long-term help into a somewhat barren organization could be from selling off two years of his top starting pitcher for a bonanza of a return package.

“With Dylan Cease, there’s not a club that (doesn’t) have a level of interest,” Getz said. “But there’s a pace to these things. I’ll continue to take the calls and certainly compare different opportunities for, perhaps, getting better.

“The starting-pitching market is always an area in which teams are looking to dive into to improve their club, and Dylan’s right at the top.”

While much of the immediate focus will be on who the retooling White Sox might trade away, they will need to field a team in 2024, so there will continue to be players added to the roster as Getz looks to fill a large number of holes. He and manager Pedro Grifol complimented new additions Paul DeJong and Nicky Lopez as being the kinds of guys they want playing the style of baseball they want.

Look for more of those types to join up as Getz continues to focus on defensive improvement and Grifol looks to implement a faster, more aggressive style of play.

“We’re on the hunt for those type of players, and that’s what we’re looking for,” Grifol said Monday. “We spent a lot of time on makeup and how players fit into the system that we are implementing right now. … There’s players out there that we feel that if we acquire them, they fit into this style of play.

“We are on the hunt for that style player. I’m confident we’re going to get this done.”