Josh Tomlin and Trevor Bauer are giving Antonetti plenty to think about, stringing together solid starts with Triple-A Columbus.
Tomlin extended his scoreless-innings streak to 20 on Thursday against Durham, throwing a three-hit shutout in which he struck out 10. Tomlin's run dates back to April 18.
Bauer took a tough loss in a spot start against the Padres last month, giving up just one earned run and fanning eight in six innings. But he's won his last three starts with Triple-A Columbus. In 25 2/3 innings, he has struck out 28, holding opposing hitters to a .196 average and posting a 1.40 ERA.
"We obviously have a few good candidates in Columbus that are certainly deserving of it, and we'll work through that decision," Antonetti said.
Antonetti didn't rule out calling up T.J. House. House is 1-1 with a 1.59 ERA in 22 2/3 innings over four starts.
"No one start influences us too much," Antonetti said. "I think we try to look at the body of work, then look beyond that, what are the subjective comments, how are they going about achieving that performance. Josh, Trevor and T.J. have all thrown the ball well."
The man whose name comes out of the hat will start either Monday or Tuesday against the Twins.
Stephen Ellsesser is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.