7:35pm: Mark Gonzales of the Chicago Tribune is up with a story on Thome not returning. According to Guillen, the at-bats for Thome simply weren't there.
7:01pm: Joe Cowley of the Chicago Sun-Times tweets that a source with the Twins told him Jim Thome's agent spoke with Minnesota this afternoon, meaning that "it's official - Jim ain't coming back." He added that manager Ozzie Guillen has confirmed this as well.
Cowley adds that Tampa Bay and Detroit are also in the running for Thome's services, but the Twins appear to be the frontrunner.
Thome would serve primarily as a pinch-hitter for Minnesota, though he could spell Jason Kubel occasionally at DH.