But with the addition of Avisail Garcia, Jose Abreu and Adam Eaton since the July 31 non-waiver Trade Deadline, the reshaping process coming off of a 99-loss season has a few less things on the to-do list.
"Someone made the point, the last six months now we've added three position players that helped retool this offense," Hahn said on Wednesday during his Winter Meetings media session at the Disney World Swan & Dolphin Resort. "All we have to do is that a couple more times over the next six months and the six months after that, and we'll be in great shape.
"That was said only partially tongue in cheek. We don't have that much work to do, but we certainly have some other priorities we hope to hit."
What else is left to do for a team looking to go younger, more athletic and with more energy? What remains for a squad that might be a year or two overdue for a rebuild after the front office consistently went all-in for the top prize after winning the World Series title in 2005, but hasn't won a championship since?
Adding a catcher to the mix of Tyler Flowers, Josh Phegley and Hector Gimenez, who returns via a Minor League deal, remains a crucial target. The White Sox strongly believe that there is untapped potential and ability with this trio, but they almost certainly won't go into Spring Training with just this group.
Thursday morning's Rule 5 Draft could be a source of help, with MLB.com's Jonathan Mayo listing Nationals catcher Adrian Nieto as one of 10 players to watch. Nieto has moved beyond a 50-game suspension, and hit .285 with 11 homers and 53 RBIs in the Carolina League last season followed by a .271 clip in the Arizona Fall League for the switch-hitter.
During a Wednesday appearance on SiriusXM radio, Hahn listed an ideal catching match as an impact middle-of-the-order, controllable, preferably left-handed bat, and then laughed and said the hosts should let him know if they knew of any. The White Sox still are thinking more along the lines of everyday player in their backstop pursuit.
"We're always shooting for long-term fits or solutions and not until we exhaust those possibilities do we turn to interim or complementary pieces," said Hahn, who explained he was "wishcasting" on the show about the catching need and not to take it out of context. "Even after that, we don't stop looking for long-term solutions.
"Again, there are a handful of items still on the wish list. I don't know how many of those long-term fits we'll be able to fill in the next 24 hours, let alone the next couple of weeks, but we're going to stay on it."
With the addition of the fleet-footed Eaton, which has the organization almost giddy, the White Sox will look to move either Alejandro De Aza or Dayan Viciedo. Both are arbitration-eligible. Both have decided upsides, and both have reasons for concern.
Viciedo, 24, begins his third full season in the Majors and has the ability to carry an offense during one of his patented hot streaks. He also has a somewhat wild strong that is hard for him to control at times.
"He has the tools to do it," said White Sox manager Robin Ventura of Viciedo. "We're looking at a kid that's continuing to grow and get better. We just want it, I think everybody just wants it now. Everybody has their growing pains and being able to get there, but he does have the tools to do it."
De Aza's offense served as one of the consistent bright spots during a poor 2013 performance with the bats. But De Aza had troubles defensively in center, and struggled mightily on the basepaths.
Moving Viciedo and the addition of Eaton sends De Aza to his more comfortable left-field spot. A trade involving De Aza still could give the White Sox a chance to platoon with Viciedo with Jordan Danks or even a more long-shot candidate such as Jared Mitchell, who is coming off of an encouraging Fall League showing after a troubling '13 Minor League campaign.
Jeff Keppinger also stands as a trade candidate, if the White Sox can find a market for a versatile infielder who is owed $8.5 million over two years and posted a .283 on-base percentage during his White Sox debut. On the flip side, all three of these players could return and contribute to the reshaping.
This plan won't be done when the Meetings end Thursday. It might not be completed until SoxFest in January or even well into the '14 campaign. Hahn actually has a barometer on how to gauge when the rebuild is complete.
"Once there is a parade," Hahn said. "Then we'll get going on the next one.
"Historically, I always felt on Wednesday of the Winter Meetings was the time we got close to doing something and got excited, only to all go to sleep and wake up prior to the Rule 5 Draft and find out that it all fell apart. We haven't gotten to that portion of the Meetings yet, but there certainly are things we're considering."