CHICAGO -- Dane Dunning, the White Sox No. 6 prospect per MLB Pipeline, departed with right elbow soreness from his start for Double-A Birmingham Saturday, according to the team.
Dunning left with two outs in the fourth inning after allowing one earned run with four strikeouts and four walks.
"Everybody considered it a very moderate strain," said White Sox manager Rick Renteria of Dunning. "Nobody is at this point too concerned."
The 23-year-old has a combined 2.71 ERA over 15 starts for Class A Advanced Winston-Salem (four starts) and Birmingham (11) this season, recording 100 strikeouts and 26 walks in 86 1/3 innings. Dunning will continue to be evaluated and undergo a MRI in the next few days.
"They still have to re-evaluate more," Renteria said. "We won't know more until they get further evaluation and at that point everybody will know where he's at. Right now he still has to be re-evaluated."
Covey improving
Dylan Covey, who was removed in the fifth inning of Saturday's 7-6 loss to the A's with what has been described as right hip flexor soreness, termed Sunday a very good day when speaking after the White Sox 10-3 victory.
Covey has Monday off but expects to throw on Tuesday prior to the series opener with the Twins.
Reynaldo Lopez, James Shields and Lucas Giolito will start the next three games for the White Sox against the Twins. Covey would be scheduled to go Friday in Texas, but the team could bring back Carlos Rodon on regular rest with Monday's off-day and give Covey an extra day.

Soria becoming trade candidate
In the month of June, Joakim Soria has gone 7-for-7 in save opportunities and has fanned 12 with one walk over 9 2/3 innings. He made his 11th straight scoreless appearance, covering 10 2/3 innings overall, in Game 2 of Friday's doubleheader and has allowed just one unearned run over his last 14 appearances.
Opponents are 5-for-46 with two walks and 15 strikeouts against Soria during that span. Soria also has a 1.84 ERA and .220 opponents' batting average over 15 appearances on the road this season.

All of these numbers make the 34-year-old veteran with 215 career saves a prime trade candidate for the rebuilding White Sox.
It's a fact definitely crossing Soria's mind.
"Players say they don't think about it, but you have to think about it," Soria said. "When you have a family with three kids and a wife you have to be prepared for everything. But it's not like I come to the field thinking about that. It's just God's plan, and whatever happens it's a business and you prepare.
"That's something I can't control. Obviously, I have a really good relationship with these guys and the chemistry with this team is very good. I can't think outside of the box because it hasn't happened yet. You have to keep focused and be ready for today's game."
Third to first
• Right-hander Miguel Gonzalez, out since April 22 with right rotator cuff inflammation, threw three scoreless innings in his first injury rehab start for Triple-A Charlotte on Sunday. Gonzalez struck out one, walked one and allowed one hit among his 37 pitches and 26 strikes against Toledo. Eloy Jimenez, the White Sox top prospect per MLB Pipeline, also hit his first homer since being promoted to Charlotte on Thursday.
• Tim Anderson, with 13 home runs and 15 stolen bases, is one of seven players in the Majors this season with at least 10 home runs and 10 stolen bases.