Gordon Beckham is the least conscionable name among the Chicago White Sox players on the trading block. John Danks, Carlos Quentin and Gavin Floyd are more likely to attract buzz. Also, these players are more likely to bring high prospects to the White Sox. Even Matt Thornton, rumored by ESPN to be actively on the trading block, has more measurable trade value than Beckham.
The White Sox have only been rumored a couple of times to be attempting to move Beckham. The Toronto Sun noted that Kenny Williams mentioned Beckham in trade talks with the Toronto Blue Jays before dealing Sergio Santos to the Blue Jays for Nester Molina. CBSSports.com mentioned Beckham among those who the White Sox are open to trading.
However, as the blog noted, Williams wants a player who could contribute immediately at the major league club in return for the players on the block. That poses a significant problem for Williams in trade talks that would involve Beckham. Getting a major-league ready player in return for Beckham is difficult.
Trading Beckham for major-league talent is difficult because of his hitting numbers. Someone like Beckham with an on-base percentage lower than .300 won't net much. Teams would want someone who they know can hit well enough to stay around. The Blue Jays might not have liked the idea of trading for Beckham with the possibility of him not being able to hit his weight.
While Blue Jays second baseman Aaron Hill did worse than Beckham at the plate in 2011 (.270 on-base percentage, 26 points lower than Beckham), the difference isn't substantial.
Also, while Beckham is one of the best fielding second basemen in the American League (second in fielding percentage and fourth in range factor per game for second basemen), it's not like teams trade for defense. This isn't the NBA. Teams want someone who can make a difference at the plate.
His poor hitting hinders the ability for Williams to acquire significant talent in a trade involving Beckham. The White Sox likely would end up shelving the prospect received in a Beckham trade in Single- or Double-A, with a low chance of seeing the player reach the majors.
If getting major-league ready talent, or something close, is a sticking point for Williams, then Beckham won't be dealt.
Anyway, don't expect to see Beckham leave the White Sox. He's not that attractive a trade target. Besides, he has only been linked to the Blue Jays thus far in trade rumors. White Sox fans should have higher hopes for him improve his hitting than see someone else rise up in a Beckham trade.