NATIONAL HARBOR, Md. -- What does Rich Hill have in common with a cadre of impressive young minor league talent in the Los Angeles Dodgers’ system?

It could be a continued presence on the Dodgers -- after the starter’s three-year deal with the club was made official Monday. The deal figures to keep those prospects with the team instead of moving on to, say, the American League, possibly for Chicago White Sox ace pitcher Chris Sale.

Hill is left-handed, and potentially adding another lefty in Sale via a blockbuster trade would add to the club’s southpaw logjam. Clayton Kershaw, Scott Kazmir, Alex Wood and Julio Urias also are left-handed starters on the roster, although Kazmir has been the subject of trade rumors. The oft-injured Hyun-Jin Ryu, another lefty starter, is also under contract for two more seasons.

Of course, Kershaw and Sale are good enough to transcend things like labels and pitching roles based on what arm they throw with. Combining that with the Dodgers’ known reticence to deal away high-level prospects and the club’s interest in locking down Hill at this point of the offseason -- before the winter meetings stew really gets thick -- could indicate they have moved on from the White Sox’s high asking price for Sale.

There was no doubt the White Sox were going to ask for the moon in order to acquire one of the best pitchers in the game, who is connected to an extremely team-friendly contract that runs through 2019 if two affordable club options are exercised. And White Sox chairman Jerry Reinsdorf revealed Monday just how super that moon is expected to be.

"You have to have four prospects who can’t possibly miss to get one," White Sox chairman Jerry Reinsdorf told Comcast SportsNet Chicago’s Chuck Garfien. "I’ve seen so many players over the years who were going to be phenoms, they were going to be future Hall of Famers, and we don’t even remember what their names are anymore.

“That’s why when you’re trading a player of stature, you’ve got to get multiple can’t-miss prospects back. That’s why it makes it tough to trade a player of great stature.”

That means that the White Sox want at least four can’t-miss prospects. The Dodgers do have four, but the odds of them parting with that many never seemed to be an option.

Yes, Sale is among the best pitchers in the game. Yes, the White Sox are well within their right to ask for so much -- and probably will get something close to it eventually. And Yes, Sale, in a rotation with Kershaw and Hill, would frighten any opponent.

The Dodgers, though, are in the process of building a young core with cost certainty moving forward, and moving four top prospects to get Sale, like perhaps Cody Bellinger, Alex Verdugo, Willie Calhoun and Julio Urias or Jose De Leon is not how the Dodgers are doing business these days.

For those not paying attention, the Dodgers are building a club for sustained success over a long period of time and are not looking to risk that chance for a quick grab at glory.

The Dodgers had plenty of enticing offers in the recent past to move guys like Urias and shortstop Corey Seager. Those guys remained, though, and are now ready to form the core of the roster.

And don’t expect the Dodgers to say they are no longer interested in Sale. They also do not figure to hang up if the White Sox happen to call them, but rumors linking both clubs might slow ... at least for now.

While there are few that believe Sale and Hill are capable of dominating an opponent equally, the Dodgers are more than pleased with the lefty they just re-signed.

“Whenever we're going through that process, we spend a tremendous amount of time digging into a guy's makeup, what type of competitor they are, what type of teammate, and everything we got back on Rich was off the charts,” Dodgers president of baseball operations Andrew Friedman said. “But I think being around him for the three months we were, it exceeded even what our expectations were. So that, in part, is what gave us the confidence to bet on him.”

The Dodgers also consider Hill and Kershaw the perfect mentors for the pitching youth movement that is to come. They could not be more pleased that Urias, De Leon, Ross Stripling and Brock Stewart and learning from two of the hardest workers in the game. There is value in that too for the Dodgers.

And even if there was a five-man rotation of left-handers that Dave Roberts had to account for next season, he would not object. He would be more than willing to find a way.

“I think that guys like Clayton and Rich, and even Julio, I don’t think the left-handedness worries us,” Roberts said. “It’s just about getting quality arms at the top of the rotation. So we’ll take Rich and Clayton against anyone.”

Yet, there is a sense with the Hill deal that the Dodgers have moved on from the Sale sweepstakes. The reason would be more prospect-based than left-handed based, but whatever the case, the club won’t look at Hill over Sale as the consolation prize.

“There aren't 10 guys that I've been around in my career that ranked as highly as Rich does in terms of having that truly innate, burning desire to win,” Friedman said. “That's something that, as we're looking to continue to further the culture that we're creating, he's going to continue to be a significant part of that.”