A source confirmed the interest, which was first reported by SI.com.
Garcia is related to Guillen by marriage. The pitcher's wife is a cousin of Guillen's wife Ibis. Guillen, though, said last week that he had not talked to Garcia "for a long time."
When talking about Garcia last Thursday, the day before SoxFest began, Guillen sounded as if the White Sox had moved on. He seemed more concerned that the team that ended up signing Garcia would be patient with some inevitable spring-training struggles.
The New York Yankees and Baltimore Orioles reportedly had interest in signing Garcia, who is considered, in some circles, as the best remaining free agent still on the market. Both teams are still considered to be interested.
Questions remain on how Garcia will be used the entire season if signed by the White Sox. He would be the obvious replacement in the rotation for Jake Peavy, who is out until at least late April after having July surgery to re-attach a shoulder muscle.
But what happens to Garcia once Peavy comes back? Guillen has said that Garcia is better suited to be a starter, which would seem to eliminate the option of putting him in long relief.
Then there is also the added implication of what the club's renewed interest in Garcia might mean. Could it be that Peavy's return is now thought to be later than expected? Or could it mean that Edwin Jackson, or even Gavin Floyd, are being considered in a trade?
Moving a starter and replacing him with Garcia would seem to be a risky proposition, but this is a team that trusts his abilities.
"People don't like the way Freddy goes about his business because they don't know him," Guillen said of other clubs. "When he went to the Mets I knew he was going to get released because they don't know him. Last year he gave up 30-something runs in two games in spring training. Well, we [knew] what we [had]."
Doug Padilla covers the White Sox for ESPNChicago.com and ESPN 1000.