Dunn is due nearly $20 million on his contract through the end of 2014, which likely kept teams from placing a claim on the slugger. The lefty could help a team looking for a designated hitter if the White Sox can work out a deal.
Dunn enters Friday batting .227/.332/.465 with 26 home runs, but has hit .297 since the All-Star break. The Rangers and Orioles may be interested in adding a designated hitter, according to Heyman, although Texas has a greater need for a right-handed hitter.
The Rangers are hoping that Lance Berkman will return from his injuries in the next ten days. If Berkman is unable to make a healthy return, Texas will have a need for a power-hitting DH. Orioles designated hitters have hit .227/.272/.383 this year and have the second lowest OPS among AL teams.