The Rangers have a team option on Rios for next season and general manager Jon Daniels has said that he's open to picking it up. However, Daniels has also said that he's open to trading players who will become free agents after the season.
Rios, who has a .293 batting average with four homers and 45 RBIs this season, was the subject of speculation before the July 31 non-waiver trading deadline.
"I'm not off the hook yet," Rios said on Aug. 1. "There's still another month to go, but I'm content and focused on the things I have to do."
Rios also said then that he had hoped to return to the Rangers in 2015.
"I don't have to prove anything," he said. "I've played this game for quite a bit now. I think I've had an OK career. It's their decision whether they want to bring me back or not. I'm not here to judge; I'm here to focus on playing the game. If they have plans for me, that's great. If they don't, that's their opinion or their way to see things. I'm here to play the game."
In other Rangers moves, catcher Chris Gimenez has been removed from the paternity leave list and designated for assignment as Geovany Soto is eligible to be activated from the disabled list Friday before the opener of a weekend series in Houston.
Gimenez went on paternity leave Monday, and remained on that list for the maximum three days even though his wife has yet to give birth. The Rangers have 10 days to trade, release or outright him to the minor leagues.
Gimemez hit .262 with 11 RBIs in 34 games over two stints this season with the Rangers.
The Associated Press contributed to this report.