Morton is rejoining the club in Texas, and will throw the bullpen session at Rangers Ballpark to test how his left foot -- his anchor foot in the delivery -- feels.
The right-hander had returned to Pittsburgh soon after leaving Sunday's game at Busch Stadium after 1 2/3 innings, when the left-foot discomfort was triggered as he ran to cover home plate after unleashing a wild pitch.
A baseball source confirmed the issue was plantar fasciitis, the sole-heel inflammation known to have given Morton a little trouble in the past.
"Of course he wants to give it a try," said manager Clint Hurdle. "Everybody wants to keep going at this point of the season. But he won't really know how he feels until he gets on the mound and tests it."
Rodriguez threw an encouraging side session in Busch Stadium on Sunday, after having felt a little soreness following his three-inning rehab start Friday with Triple-A Indianapolis.
Upon the club's return home, the lefty is to pitch a simulated game Thursday morning in PNC Park, a four-inning exercise intended to stretch him out to 65-70 pitches. He had thrown 48 in his start for the Indians.
Tom Singer is a reporter for MLB.com and writes an MLBlog Change for a Nickel. He can also be found on Twitter @Tom_Singer. This story was not subject to the approval of Major League Baseball or its clubs.