"[Perez) ]is getting better," Yost said. "[The swelling] is diffusing. It was a pretty big area [softball size] and it's getting smaller, about half that."
The intercostal is a series of muscles within the rib cage that serve to support the chest wall. Perez sustained the injury while swinging and missing on a ball in the dirt.
Perez is on this road trip that continues in Chicago on Friday and concludes in Oakland.
"[Trainer Nick Kenney] is hoping to have him pain-free in seven to 10 days," Yost said. "It might be a little quicker, like seven days. He's making progress.
"[Kenney] said the worst-case scenario was four weeks originally, but it looks more like two or three weeks. It's what we kind of expected."
The key, Yost said, is to make sure Perez doesn't push his recovery to the point he doesn't heal properly.
"We all want to push it," Yost said. "But we got to do it right."
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.