Dunning (shoulder) threw a bullpen session on Tuesday, Jeff Wilson of RangersToday.com reports.
Dunning (shoulder) threw from 90 feet Monday, Shawn McFarland of The Dallas Morning News reports.
The Rangers placed Dunning (shoulder) on the 15-day injured list with a right rotator cuff strain.
Rangers manager Bruce Bochy said Wednesday that Dunning will be placed on the 15-day injured list with a shoulder issue, Kennedi Landry of MLB.com reports.
Dunning (3-2) earned the win after he pitched 5.1 innings, allowing two runs (one earned) on three hits while striking out 10 in Sunday's 4-3 win over the Reds.
Dunning came away with a no-decision in Wednesday's 5-4 win over the Tigers, giving up two runs (one earned) on three hits and four walks over five-plus innings. He struck out five.
Dunning allowed one unearned run on three hits and one walk while striking out eight over five innings in Wednesday's spring start against Cincinnati.
Dunning said Sunday the new pitch he's working on this spring is a forkball, Kennedi Landry of MLB.com reports.
Dunning allowed two runs on two hits, a walk and a hit batsman while striking out two over two innings in Tuesday's spring start against the Diamondbacks.
Dunning threw one scoreless inning in Friday's spring start against the Royals.