SAN DIEGO -- White Sox general manager Rick Hahn and executive vice president Ken Williams had dinner Tuesday night and then met again Wednesday morning.

Nothing out of the ordinary there. Certainly not in the context of the 2019 Winter Meetings. But in this specific instance, Hahn had trade discussions potentially influencing the present and the future of the franchise to hash out, talks seemingly affecting the immediate direction of the franchise's rebuild.

"We've got some prospects that are extraordinarily popular and a few things that at least made us take a step back and pause and think, 'Is this consistent with what we started three years ago?'" Hahn said. "Or is this an effort to force things a little more quickly?

"There's been some temptation around. But again, we're trying to stay true to what we set out to do three years ago, and what we do feel we're getting awfully close to being able to enjoy the fruits of."

Since the team's rebuild began with the trade of Chris Sale to Boston three years ago at the Winter Meetings, moves made by Hahn and the White Sox have been targeted for sustained success and not toward any sort of quick fix. That rebuild has moved from the strictly developmental phase into a potential contention phase in 2020, with a target of '21 for prime contention.

Young players such as first baseman Andrew Vaughn, right-hander Dylan Cease and second baseman Nick Madrigal figure prominently into that future planned championship picture. But maybe that temptation has come through proposed deals involving one or more of these highly touted prospects.

As Hahn pointed out, they hadn't quite found the right fit so there was nothing to announce. Instead, Hahn focused on the move to acquire right fielder Nomar Mazara via trade from Texas late Tuesday in exchange for Minor League outfielder Steele Walker.

It was a deal drawing decided mixed reaction from the fan base, who were looking for a Nicholas Castellanos/Marcell Ozuna sort of splash in terms of right-field improvement. Hahn stressed a big-picture view of the individual trade while pointing out the positives surrounding the 24-year-old Mazara.

"We view him, our scouts view him, as someone who has some untapped potential and some upside," Hahn said. "But I think it needs to be understood that even on the downside of this ... let's say he's the same player he's been for the last couple years at the big league level, having a bat like that against right-handed pitching in the lower third of our order, which is where he may well end up, has a lot of value.

"I wouldn't judge this move necessarily in isolation. I'd wait to see how the entire roster pans out and what we have, ultimately, on a day-to-day basis come this summer.

"This is a kid who, as you all are aware, has been viewed as having a very high ceiling," Hahn said. "We continue to think he has a chance to reach that ceiling and are optimistic about where he goes once he's with us. But if he continues on the same path he's been on for the last few years, that's a valuable bat with good defense, especially against right-handed pitching."

Acquiring starting pitching remains a priority for the White Sox, but they aren't done adding offensively. Mazara is a strong presence against right-handed pitching, but with just a .231/.272/.361 career line against southpaws.

Maybe the White Sox can find pitching and a complement for Mazara in the same deal. Hahn said of the 20 Winter Meetings he's attended as part of the White Sox, surprise deals have arisen somewhere around 12 times on Wednesday night, only to be gone by Thursday's Rule 5 Draft. He even joked that the surprise came one night early this year.

So on Wednesday the focus was on Mazara and his fit on the new team.

"We're better today. We've got a 24-year-old, 25-year-old left-handed-hitting outfielder who can do some damage against right-handed pitching," Hahn said. "We don't have that yesterday and it came at a cost we were comfortable with paying.

"Whether ultimately that's satisfying in terms of the final roster and the role he plays, that remains to be seen. I do know this team's better today than it was yesterday. Continue to do that. You do that enough times over the course of the offseason, and you get yourself a pretty good position."