"Both Francisco and Hanson essentially had to go to extended [spring camp] to build up arm strength and now join the [Charlotte] club and are still sort of building up their in-season regimen," Hahn said. "Hanson has had two starts, and he's progressing really well.
"All three of those guys could very realistically be factors," Hahn said.
The White Sox 40-man roster sits at 40, meaning a corresponding move would be needed if one of these three eventually were added.
Scott Merkin is a reporter for MLB.com. Read his blog, Merk's Works, and follow him on Twitter @scottmerkin. This story was not subject to the approval of Major League Baseball or its clubs.