The seven-year, $69.835MM extension that Alex Rios signed with the Blue Jays back in 2008 didn't initially contain no-trade protection, but a limited no-trade clause allowing Rios to block trades to six teams kicked in starting in 2009. Mark Gonzales of the Chicago Tribune reports that the six teams to which Rios can block a trade are the Yankees, Diamondbacks, Rockies, Royals, Astros and Athletics.
The Rockies, Diamondbacks and A's are likely set on outfielders, and the Astros certainly aren't looking to buy at this time. However, the no-trade protection against the Yankees and (to a lesser extent) the Royals is significant, as both teams would make sense as suitors for Rios.
The struggling Yankees scored fewer runs than any team in baseball last month (88) and have a dearth of right-handed power. Offense is said to be New York's primary need in trades. The Royals opened the season with Jeff Francoeur in right field but have since designated him for assignment. Recent reports did state that the chances of Kansas City making a big move were "slim," and David Lough has played well in place of Francoeur.
Nailed it.