Earlier this month, the White Sox broke new ground by being prominently linked to an international player who might blow out their budget. Baseball America’s Ben Badler linked the Sox to Cuban outfielder Luis Robert, and Badler doesn’t make these connections lightly. Once they stick, they tend to stick.

Reporting from Robert’s open showcase in the Dominican Republic on Thursday, the White Sox are sticking:

Nearly all teams appeared to have someone there (and many of them had multiple club officials on hand), though the teams over their bonus pool and the White Sox are the ones that appear the most likely to sign Robert.

The over-their-pool teams include the Cardinals, Astros, Reds, Padres and Athletics. None of them are big spenders, and all of them kinda make the White Sox look even weirder for adhering to the strict spending limits before the league cracked down on it with the most recent CBA. That said, the White Sox’ previous reluctance has afforded them the opportunity to pursue the 19-year-old, 6-foot-3-inch center fielder, at least if he’s clear to sign by June 15. Should his situation bleeds into the next signing period and its heavily enforced spending caps, Badler says the White Sox have the room to accommodate him there, too, but it wouldn’t be as uncharacteristic given the new rules.

The White Sox have set up a private workout with him next week, and if Marco Paddy — who was in attendance — is able to convert, it’d be the equivalent of adding a first-round pick to the farm system based on Badler’s early-March scouting report:

Robert has the talent of a first-round pick if he were in the draft. After he signs, he should be ready for an assignment to a low or high Class A affiliate. He has a strong, lean frame at 6-foot-3 with broad shoulders, a wide back and quick-twitch athleticism. A righthanded hitter with excellent bat speed and a sound swing, Robert has plus power with room to continue filling out and increase that in the future. [...] Robert’s production does come with some swing-and-miss tendencies. He has a habit of swinging through high fastballs and has had trouble laying off breaking balls down and away, though at times he’s shown the ability to resist those pitches. He can hammer pitches to right-center field and is at his best when he stays through the middle of the field, but he can get too pull-oriented in games.

It was only the day before that Badler reviewed the other international players signed by the White Sox during this period, led by a trio of corner outfielders.

*Josue Guerrero, OF: Badler draws a connection to Fernando Tatis Jr., in that the White Sox were more excited about him than the rest of the league when they signed him for $750,000 in 2015. It’s the same story for Guerrero, whom the White Sox signed for $1.1 million. He’s a power-hitting righty whose family has a history of late-developing toos.

*Luis Mieses, OF: A “long, lanky left at 6-foot-4, 185 pounds with intriguing offensive upside,” the White Sox signed him for $428,000. Given that he’s only 16, his frame has plenty of projection left, which makes it all the more interesting that he has already shown in-game power.

*Anderson Comas, OF: Badler connects him to Gregory Polanco, both due to his trainer, his left-handedness and his skinny frame (6-foot-4, 180 pounds). Unlike Guerrero and Mieses, he has an easy line-drive swing, and the hope is that the strength comes later, since he’s a corner outfielder who doesn’t yet run or throw well. The Sox signed him for $425,000.

*Jendersson Caraballo, RHP: A 17-year-old Dominican signed for $350,000, he touches 92 with his fastball and throws a power slider to go along with a nascent changeup.

*Lenyn Sosa, SS: His hit tool and arm strength drive his value more than his range and power, but the White Sox think the 17-year-old Venezuelan can stick at shortstop. He signed for $325,000. Badler says “some teams looked at Sosa’s skill set and hard-nosed mentality and wondered whether he could transition to catcher.” (The White Sox put a different Venezuelan behind the plate instead. Kleyder Sanchez auditioned as an outfielder, but the Sox signed him as a catcher for $50,000.)

*Anthony Coronado, OF: The 17-year-old Venezuelan rounds out the group of six-figure signings at $150,000, and the right-handed hitter has “solid tools and a chance to play center,” which makes him stand out from the other outfielders ... at least assuming Robert doesn’t close out this group.