Here's another team that has shown some interest in Rios: the Royals.
The Royals have been talked about more as a possible trade-deadline seller, and sources have said they would at least listen if teams want to discuss pitcher Ervin Santana. But the Royals have also been looking to add, looking particularly at under-control players who would fill their needs in right field or at second base.
Rios is signed through next year, with an option for 2015, so he fits in that way. A deal could be complicated by the fact that the two teams are in the same division. It's not clear how much they have talked.
Scouts who have watched Rios recently say he doesn't appear to be playing with any energy, comparing it to his final days with the Blue Jays. White Sox manager Robin Ventura pulled him out of a game last Friday after Rios didn't run hard to first base.
As for Santana, while the Royals will definitely listen, they don't seem overly motivated to trade him. While Santana can become a free agent at the end of the year, the Royals are said to have some interest in trying to re-sign him. They also see interest in finishing this year strong.