"We'll go day to day until we know what he can handle," manager Ron Washington said.
Choo, when he hasn't been used at DH, played exclusively in left field before the All-Star break. But he has been used more in right field since Rios originally injured the ankle on July 19 in Toronto.
"I'm more comfortable in right field," Choo said. "I missed a ball there [Tuesday] but I'm more comfortable there. I played right field all six years in Cleveland. I like playing just one position, but I understand the situation. I wouldn't mind playing center field if they need to give Leonys [Martin] a day off."
On Tuesday night, Choo was thrown out in the seventh inning trying to score from second base on Elvis Andrus' one-out groundball single to right field. Washington said the ankle was not an issue on the play.
"He didn't get a good jump and then looked back while he was running," Washington said. "That took away from him."
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.