At the trade deadline last year, the Chicago White Sox were one of the teams that were showing very serious interest in acquiring Adam Dunn. They were prepared to offer the best (depending on who you ask) pitching prospect in their minor league organization, but the talks fell through when the Nationals asked for second baseman Gordon Beckham.
Now that the White Sox don't have to part with any prospects at all to get Adam Dunn into their lineup, they seem to be showing serious interest in signing him.
The Chicago White Sox have jumped in on free agent Adam Dunn, according to sources. Kenny Williams' interest appears serious
If Dunn goes to an AL team, of which the White Sox are, it means that he has likely wavered somewhat on his stance toward playing DH. He has said in the past that he would not want to go to a team that would use him primarily as a designated hitter, but that is probably where he would fit in with the White Sox and where the greatest market for him would be.