Texas has been looking for a right-handed hitter, most likely a right fielder, and in a thin market Rios would appear to be at or near the top of it. Texas, and several other teams recently have scouted Rios (the Pirates are one, and Danny Knobler of CBSSports.com identified the Royals). Rios is available along with almost all the White Sox.
Ideally, Texas would have loved to make a run at young Marlins superstar Giancarlo Stanton, Hunter Pence (a local, being a U-T Arlington product) or perhaps Michael Cuddyer, but with those three apparently unavailable at the moment, the Rangers are surveying a market that's heavy on far lesser talents. Pence would seem to have the best chance to be traded of those three, and Texas would target him if he becomes free. Nolan Ryan is said to be a fan.
Seattle, which has Raul Ibanez, Kendrys Morales and Michael Morse, isn't ready to trade anybody yet. And most believe they'll ultimately keep at least Ibanez and Morales now that they are showing decent signs of life.
The Rangers don't seem especially interested in a reunion with Alfonso Soriano, perhaps because right field is their preference, and he seems likely to go to the Yankees, anyway.
Texas would like to beef up its offense, anyway, but they may also have concerns about the status of Nelson Cruz, whose name has been linked to Biogenesis.
The Rangers reportedly have looked at Norichika Aoki, as well, and Danny Knobler reported they are scouting Marlon Byrd, their former player. Other outfielders who could go in trades include Justin Ruggiano, Chris Denorfia, Nate Schierholtz and Alejandro De Aza
Rios is under contract through next year at $12.5 million a year.