Garza, who is dealing with triceps soreness in his right arm, is not expected to make his next scheduled start Friday at home against the St. Louis Cardinals.
"I don't think it's going to happen," manager Dale Sveum said. "If he's not going to throw a [between start] bullpen I don't think he's going to throw Friday."
Sveum said Travis Wood will start Friday in Garza's place. With an off day Thursday, Wood will simply stay on a five-day schedule after pitching Sunday in St. Louis.
Garza left his most recent start Saturday after three innings when arm discomfort cropped up. The Cubs have been calling the problem a cramp. Sveum said that Garza is on a "dose pack" which suggests the pitcher is taking a cycle of anti-inflammatory medication.
The Cubs are still not saying that a stint on the disabled list is upcoming for Garza. As of now, the expectation is that his next outing is simply being pushed back a day or two.
The most recent trade speculation involving Garza has the right-hander being pursued by a number of teams with the Los Angeles Dodgers being mentioned most often.
Dempster was reported to be heading to the Atlanta Braves, but the Cubs pitcher said via his foundation's Twitter account that there was no trade. The Cubs said that there is no trade announcement upcoming.