Both appeal to the Rangers for several reasons. They are both right-handed hitters with power, and they are both under contract beyond this season. Rios, 32, is hitting .284 with 11 home runs, 34 RBIs and a .472 slugging percentage. He is also signed at $12.5 million for 2014 with a $13.5 million club option for '15.
Rios would have greater appeal than Willingham, but he likely would carry a higher price tag. Willingham is hitting .216 with 10 home runs, 34 RBIs and a .398 slugging percentage. He is signed for next season at $7 million. He hit .260 with 35 home runs and 110 RBIs for the Twins last season.
The Rangers called up Engel Beltre on Sunday to replace Gentry as the backup outfielder; he gives them another left-handed bat in the outfield, along with David Murphy and Leonys Martin. That leaves the Rangers' outfield heavy from the left side.
"Yes, it is a little concerning, but we'll make it work," manager Ron Washington said.
The Rangers have other long-range concerns with their outfield. They still don't know what will happen with Nelson Cruz in regard to Major League Baseball's investigation of Biogenesis, the Miami anti-aging clinic that allegedly distributed performance-enhancing drugs to a number of Major League players. Cruz is among the names linked with the clinic and could face a possible suspension pending the completion of MLB's investigation.
Cruz and Murphy are also free agents after this season. Acquiring a player like Rios would help address the outfield concerns beyond this season.
T.R. Sullivan is a reporter for MLB.com. Read his blog, Postcards from Elysian Fields, and follow him on Twitter @Sullivan_Ranger. This story was not subject to the approval of Major League Baseball or its clubs.