Both outfielders will be free agents after the 2015 season and almost certainly wouldn't fit in past the final two months of this campaign. So, how would they fit currently?
White Sox general manager Rick Hahn has talked on numerous occasions about wanting to win more than just one title and how he was focused on developing a young core that can help the big league club on a yearly basis.
To get a player such as Upton or Cespedes, the White Sox would likely have to give up a Major League-ready prospect from that young core -- a player such as Erik Johnson or Frankie Montas. In the case of Cespedes, the White Sox would be giving up those prospects to a rival within the American League Central.
Trading for an impact right-handed bat such as Cespedes or Upton could move Avisail Garcia into some sort of a platoon situation with Adam LaRoche, much like the White Sox employed when acquiring Ken Griffey Jr. at the 2008 non-waiver Deadline. LaRoche is hitting .213 with nine homers in the midst of a two-year, $25 million deal.
Team officials remain high on the ability possessed by Garcia, who is in the midst of his first full Major League season and was described as a five-tool talent by executive vice president Ken Williams at the season's outset. But Garcia has one double, one triple and no homers in the month of July.
Then there's the situation with Jeff Samardzija, who seems to be staying with the White Sox after this seven-game winning streak. But with the starting-pitcher pool dwindling as Friday afternoon gets closer, could a team make Hahn an offer he can't refuse? Could those prospects help add to a system that they could subtract from in another deal?
For manager Robin Ventura, it's the sort of situation to address when something actually happens.
"Nobody is walking in the clubhouse today that is going to help us win tonight," said Ventura on Thursday evening. "These guys are very good at focusing on today and getting through this and trying to win tonight's game.
"You don't look too far ahead. They're not focused on if we're trading somebody or if we're not trading somebody."
Scott Merkin is a reporter for MLB.com. Read his blog, Merk's Works, follow him on Twitter @scottmerkin and listen to his podcast. This story was not subject to the approval of Major League Baseball or its clubs.