Thursday's off-day enables Showalter to move Ubaldo Jimenez (3-2, 2.41 ERA) from Sunday to Saturday on full rest.
Showalter said it's possible that Norris (1-4, 9.88 ERA) could pitch Sunday's series finale. If not, right-hander Chris Tillman (2-5, 6.34 ERA) will make the start.
Norris was suffering from a stomach illness during his outing last Sunday in New York against the Yankees. He allowed four runs in 3 1/3 innings of a 6-2 loss and fell to 1-4.
On other Baltimore injury fronts, the news is more positive.
Infielder Everth Cabrera (left foot contusion) began a rehab assignment with Triple-A Norfolk on Friday night at Indianapolis, playing second base and batting leadoff. He went 0-for-3 with a strikeout.
Cabrera went on the 15-day disabled list May 7, one day after being hit by a pitch against the Mets.
Catcher Matt Wieters (rehabilitating from Tommy John surgery) took batting practice Friday in Sarasota.
"Went real well. He's really turning it loose, which is a good sign," Showalter said. "Plan is for Matt to join us in Miami next week and hopefully go out [on a rehab assignment] from there.
Infielder Jonathan Schoop (right knee sprain) will begin baseball activities on Saturday.
Harvey Valentine is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.