Dunning (shoulder) had his rehab assignment transferred to Triple-A Round Rock on Saturday.
Dunning has been on the 15-day injured list since July 5 as a result of right shoulder soreness, but he's now one step closer to his return to the big leagues. The right-hander pitched two scoreless innings in his only rehab start with Double-A Frisco on Sunday and it's possible that Dunning will only need one outing with Round Rock before being activated from the IL.