But Kennedy just came off the disabled list after a hamstring injury to make that Sunday start.
"Not sure we really want to push him," Yost said. "We'll see."
Yost also indicated that right-hander Miguel Almonte could be an option to start on Thursday. Almonte has a 1.86 ERA for Double-A Northwest Arkansas this season.
Yost said he did not want to bring back right-hander Jake Junis, who started on Sunday in the first game of the doubleheader, on short rest for a Thursday start.