FRIDAY: A source involved in the trade talks between the two sides told Jim Bowden of ESPN and MLB Network Radio that the chances of a deal are "smaller than a bread basket."
THURSDAY, 4:51pm: A trade is unlikely to be reached, writes MLB.com's T.R. Sullivan. Prior to the deadline, the White Sox were interested in lefty Martin Perez, right-hander Luke Jackson and infielder Rougned Odor, and the Rangers aren't keen on giving up those players in a trade for Rios.
3:29pm: The Rangers and White Sox "weren't even close" on an agreement when discussing Rios prior to the July 31 non-waiver trade deadline, tweets Danny Knobler of CBS Sports. Knobler also tweets that Rios was placed on waivers on Monday, and the deadline to work out a deal for him is tomorrow. That would suggest that Rios was claimed earlier in the week, but the news only broke today.
2:45pm: The Rangers are the team that claimed Rios, according to Evan Grant of the Dallas Morning News (on Twitter). Grant cautions that claiming Rios and actually striking a deal to acquire the 32-year-old are very different things.
Because he is on revocable waivers, the White Sox have 48 hours to work out a trade with the claiming team or pull him back off waivers. Chicago could also let the claiming team have Rios for nothing and be content to dump his salary -- the very manner in which Chicago acquired Rios from the Blue Jays in 2009 -- but that seems unlikely given his .277/.328/.421 batting line. Rios is controlled through 2014 and owed $12.5MM next season with a $13.5MM club option, though each of those salaries will increase by $500K if he is traded.
It seems likely that an American League team was awarded the claim on Rios, as waiver priority at this point in the season is determined by league and record. All 15 AL teams would have the opportunity to claim Rios before an NL team. The Rangers and Pirates were both connected to Rios prior to the July 31 non-waiver trade deadline.