Rios would have to waive his no-trade clause for any deal to go through, but with the chance to move to a contender he would likely do so.
A potential snag is that he suffered a minor foot injury in today's game.
UPDATE: @arios51 suffered a contusion of top of left foot in tonight's game and will have X-rays for precautionary measures.— Chicago White Sox (@whitesox) July 31, 2013
The Yankees recently acquired Alfonso Soriano from the Cubs, and have Curtis Granderson returning from the disabled list, so a move for an outfielder seems unlikely. They currently have Brett Gardner as well, which means they have good options for all three spots when everybody's healthy.
Rios, 32, is hitting his way to a triple-slash line of .272/.324/.428 in 2013, and his career numbers would suggest he should improve on that. It seems unlikely the Yankees would be able to deal for him given their lack of prospects and the fact that he would not fill an obvious hole.
The Yankees are currently 55-50 and in fourth place in the AL East.