Perez, who suffered the injury on Aug. 4, has been running and sprinting for about three days, and threw for the second time in three days.
Perez reported some discomfort when he threw on Thursday in St. Louis.
"He was doing really good and then he tried to amp it up and felt a little pain," Royals manager Ned Yost said.
But there were no issues Saturday.
"I don't feel any pain in the throwing or running," Perez said. "We're going the right way."
Perez said he is hoping he can start taking some bullpen sessions and hitting off the tee soon.
"Maybe next week we start catching bullpens and maybe start swinging," Perez said. "We'll see what the progress is by then and go from there.
"I think the first thing will be to hit off the tee. I don't know what day. We go day by day. Whatever they tell me, I'll do. So far, so good."
The intercostal is a group of muscles in the rib cage that help support the chest wall.
Jeffrey Flanagan has covered the Royals since 1991, and for MLB.com since 2015. Follow him on Twitter @FlannyMLB. This story was not subject to the approval of Major League Baseball or its clubs.