So, the left-handed combination of Thornton, Chris Sale, Will Ohman and Hector Santiago is not quite as unusual as it seems for the 2012 White Sox. Nonetheless, the White Sox could eventually choose to move a veteran such as Thornton and Ohman if the modified rebuilding process goes all in.
That possibility hasn't crossed Thornton's mind, especially with the team proving to be competitive through the first five weeks of the campaign.
"I prepare myself every day, no matter what's going on, what rumors are swirling around," Thornton said. "People probably will look into it a whole lot more than what it is.
"Right now, we are a couple of games out of first and trying to get on a run here and break our rut we've been in the last 10 days or so. But that's all we are focused on is winning ballgames. That's all I ever do, no matter what goes on."
Thornton has one year left on a two-year, $12 million extension, with a $6 million club option for 2014. Ohman is owed $2.5 million in 2012.