4:00pm: The White Sox are interested not only in Cespedes but also in the Padres’ Justin Upton, reports Jon Heyman of CBS Sports (via Twitter).

2:41pm: The White Sox are flipping the script and aggressively pursuing a bat, Bob Nightengale of USA Today reports on Twitter. Among the many players they’ve inquired about, per the report, is Yoenis Cespedes of the Tigers.

It remains unclear at present precisely where the club would like to add. Cespedes, of course, is a rental outfielder, but Chicago has received fairly marginal production at almost every spot on the diamond. First base (Jose Abreu) and center field (Adam Eaton) seem to be the only two positions where an upgrade would not make any real sense, though obviously the team is unlikely to replace veterans like Alexei Ramirez (at short) and Melky Cabrera (in the outfield). That Cespedes holds interest seems to suggest that Chicago is willing to take time away from Avisail Garcia and/or Adam LaRoche (the team’s right fielder and primary DH, respectively).

More importantly, perhaps, is the question of what kind of price the club might be willing to pay to get something done and whether the team is considering a move for controllable assets. Chicago is not exactly in an enviable position, though the team has played better of late. The division-rival Tigers are selling despite the fact that they are only one game behind Chicago in the standings. The White Sox are 11.5 games back of the leading Royals, and remain two-and-a-half out of Wild Card position.

With the team pursuing a bat, it would seem highly unlikely that righty Jeff Samardzija will be moved. That had already seemed to be the case, so perhaps it isn’t surprising to learn that the club prefers to enhance its chances with an addition, rather than simply standing pat.