Rios does have a no-trade clause in his contract, but the Giants are not among the six teams on his list, which includes the Yankees, Diamondbacks, Rockies, Royals, Astros, and Athletics.
Rios is batting .304 with four homers and 43 RBI for the Rangers this season. The Rangers acquired him in a trade with the White Sox last August.
The Giants are 58-50, and three games back of the NL West-leading Los Angeles Dodgers. They are currently tied for the first wild card spot with the Atlanta Braves.
On Saturday, the Giants traded for pitcher Jake Peavy.
- Sarah Barshop