The junior suffered a bruised right shoulder in a 30-27 loss at No. 20 Southeastern Louisiana on Oct. 1 when he was hit at the end of an 8-yard scramble early in the third quarter.
"The MRI showed he's got no structural damage. The bones, the ligaments and everything is good," Woodard said. "It's just bruised. It's going to come down to how fast he can heal, the soreness and how much he can handle so he can get the full range of motion back."
Earp was replaced by Joe Minden, who was returning from a broken right hand suffered in a 66-31 loss at Baylor on Sept. 12. The two quarterbacks split snaps in their first two games for the Cardinals (2-2, 1-1) until Minden's injury, which was initially expected to keep him out four to six weeks.
"Joe will get a bunch of reps this week, and Joe will be ready to go," Woodard said. "We'll just see how Carson does, but it's good that we got Joe back. He'll put in a good week, and we'll probably make a decision Saturday."
Earp, a junior college transfer, had four of his seven touchdown passes in a 49-46 upset of then-No. 3 Sam Houston State on Sept. 19. Minden, a senior transfer from Stephen F. Austin, has completed 70.7 percent of his attempts for 304 yards and four TDs.
With assistance from Echo Maintenance, Lamar is giving away 5,000 tickets to military veterans and their families Saturday. The school is also providing pregame meals and concerts.
"I think it's a great thing that we're doing for the veterans, and we want to go out there and play well for them," Woodard said.