Rios is one of several hitters the Rangers are looking at, a major league source said, but nothing is imminent as far as a trade is concerned. Rios spoke to the media about trade interest from the Rangers and other clubs on Wednesday.
Manager Ron Washington said before Wednesday's game with the New York Yankees that the Rangers could use a right-handed hitter in the lineup.
"We are left-handed heavy," Washington said. "We certainly want to add a big right-handed bat. What bat that will be, they're up there hunkered down right now trying to figure that out."
Rios came out hot to start the season, but his power numbers have dropped in June and July. He's batting .259 with two home runs and 16 RBIs in his last 35 games. He has a .307 on-base percentage since June 9.
Rios batted .289 with 10 home runs and 32 RBIs in his first 59 games.
The Rangers also have the possible concern of a suspension for right fielder Nelson Cruz, who is connected to the Biogenesis case.