Looks like the idea that Chicago claiming both Jim Thome and Jason Kubel to block Cleveland from either was only half-right. Turns out that the Indians were able to claim Jim Thome, while the White Sox claimed Jason Kubel, per a breaking report from Ken Rosenthal (twitter).
Buster Olney was just reporting that the Indians were discussing a trade with the Twins, and Jim Thome is apparently it. What Minnesota wants in return for Thome is not yet known, but Thome does have a full no-trade clause in his contract. Rosenthal reports that Thome would prefer to go to the Philadelphia Phillies. Circumventing the waiver process might hurt his image, though.
The Kubel-to-the-White-Sox deal is unlikely to be completed, as he's close to being a Type-A free agent and "Twins would want something significant in return." Kubel is still owed $900K on the season.
Either deal will require completion by tomorrow, assuming both were claimed yesterday. Both Thome and Kubel are free agents after the end of the season.