SAN DIEGO -- The White Sox left the Winter Meetings on Thursday morning two days removed from adding right fielder Nomar Mazara via trade with the Rangers and three weeks after signing free-agent catcher Yasmani Grandal.

But White Sox fans wanted more and still want more as the end of 2019 approaches. General manager Rick Hahn understands the urgency.

"I'm the same way. We have the same motivation in the office," Hahn said, addressing the media after the Major League phase of Thursday's Rule 5 Draft. "If we have three or four needs and we get them all done the way we want with our priority targets in November, fantastic.

"You can't force the pace of this. And certainly, if we hit on the right targets, come next June or July, nobody's going to have any issue with whether we acquired them on Dec. 13 or we acquired them on Jan. 13."

Hahn stressed progress was made at the Winter Meetings on a handful of fronts, even if the Mazara trade and iconic broadcaster Ken "Hawk" Harrelson being named the 2020 Ford C. Frick Award winner emerged as the team's only news from the Manchester Grand Hyatt.

"Obviously, the pitching need is the one that's most prominent right now," Hahn said. "We've had productive conversations with agents and with other teams about potential trade fits, and we'll just have to see how quickly we're able to come to a meeting of the minds there.

"Obviously, there's going to be future moves over the next couple of weeks. Hopefully we'll line up sooner rather than later."

BIGGEST REMAINING NEEDS

1. SP: Zack Wheeler picked the Phillies, but the White Sox have moved on from their top choice and their five-year, $125 million offer. Even if they aren't committed to giving the required years and money to starters like Dallas Keuchel or Hyun-Jin Ryu as part of their current rebuild phase, there are other options. Those options could include trades.

"Absolutely. You've seen over the years us use our financial flexibility to acquire some contracts," Hahn said. "That flexibility doesn't always have to be spent on free agents."

2. DH/RF: As of mid-December, Mazara is the team's starting right fielder. His career splits against righties are much stronger than against lefties, so a right-handed-hitting complement could be added. The White Sox also could bring in more power at the designated hitter's spot, using switch-hitter Leury García in a quasi-platoon with Mazara.

3. SP: Yes, the White Sox need two starting pitchers, even with young hurlers such as Lucas Giolito, Dylan Cease and Reynaldo López in place and Michael Kopech on his way back after Tommy John surgery in September 2018. The second starter acquired also could be someone used to help solidify the bullpen in a swing role.

RULE 5 DRAFT
The White Sox selected right-hander Will Carter (Yankees) in the Triple-A phase. The organization did not lose a player in the Rule 5 Draft. Carter, 26, has a 9-15 record with a 4.61 ERA over 95 Minor League games (40 starts). He has 181 strikeouts, 140 walks and a .265 average against over 290 2/3 innings. The Yankees took him in the 14th round of the 2015 Draft.

GM'S BOTTOM LINE
"I walk out of here enthused that I know we are better today than we were at the start of the offseason. I suspect by the time we get to Spring Training, we are going to be better than we are today. This whole process started about three years ago now. We are thrilled with how much progress we've made. We are impatient about getting to that most rewarding stage of this rebuild when we are ready to win. We think we've taken steps to get that closer." -- Hahn