Mark Gonzales of The Chicago Tribune tweets that White Sox GM Kenny Williams had thoughts about approaching free agent Jermaine Dye, but the White Sox have a greater need for a left-handed bat.

Dye, 35, had a great 2009 campaign for the White Sox. He hit 27 home runs drove in 81 RBIs. The White Sox declined the $12 million team option on Dye in November and paid him a $950,000 buyout. He has drawn interest from the New York Yankees, San Francisco Giants, Texas Rangers, Boston Red Sox and St. Louis Cardinals this Winter, but no offers were made. You can see Dye’s contract history and statistics here.