Williams called free-agent Paul Konerko his No. 1 priority now, just moments after the team agreed to a deal with Dunn that will be made official Friday after a physical exam.
"Not only is there still room for [Konerko], it would be the perfect fit from our perspective," Williams said Thursday. "But we can't get too far ahead of ourselves. The one thing Paul and I talked about at the end of the season was to be respectful of each others' positions and be mindful that there is a process."
So what is that process?
For Konerko's camp, that seems to be a deliberate pace of going through the winter meetings to make sure all options have been explored. For Williams, it was a plea for understanding that if he started moving things at a quicker pace it shouldn't be seen from Konerko's side as an ultimatum.
"I've never been accused of being the most patient person," Williams said. "I have a commitment to the organization and the city to put a good team on the field, but it's a fine line to be respectful of [Konerko's] process and be cognizant of putting the best baseball team on the field."
Konerko negotiations, meanwhile, haven't gone anywhere as the White Sox wait for Konerko's agent, Craig Landis, to open the door to talks.
"That's something we've tried to initiate on a few occasions," Williams said. "We respect Paul's decision to try to take things through the winter meetings and flush out the interest and the offers. We're trying to be patient and respectful of this process but also mindful of [potential] lost opportunities for another player if we're not able to bring back Paulie. I've made no secret we do have strong interest [to] bring him back."
It has been reported in some circles, though, that the Baltimore Orioles have already made a significant offer to Konerko.
It's possible the Dunn deal would help. If manager Ozzie Guillen slides Dunn into the No. 5 spot in the lineup, Konerko might find it too irresistible to return to his spot as the White Sox cleanup hitter.
But signing Dunn and bringing back Konerko begs the obvious question. Since Dunn will make a reported $56 million over four years and Konerko figures to earn at least that much, are the White Sox operating on a different budget from the one they originally thought they would take into the 2011 season?
Williams said that instead of the three or four offseason agendas he usually presents to chairman Jerry Reinsdorf, he had just two this time. One was a young team that, while more affordable and full of potential, would take its lumps. The other was to add to what existed.
"Ultimately [with the Dunn deal], you see the obvious decision," Williams said. "We just didn't want to be in the middle. The decision was that if we were going all in, we were going all in. It's been difficult to find the revenue to support the payroll, but we're out there on a limb. We think it's important to make a significant addition."
Doug Padilla covers the White Sox for ESPNChicago.com and ESPN 1000.