The tests measure a player's cognitive skills before and after a concussion. A player is allowed to return only after his tests return to normal and he shows no signs of having had a concussion.
If neither Moore nor Redman can play, rookie Jonathan Dwyer might be needed Sunday night against New England (6-2), which won the past two times it played in Pittsburgh.
The Steelers (6-2) had numerous injuries during their 27-21 victory in Cincinnati, including a sprained right knee for left guard Chris Kemoeatu. He could be limited in practice.
"We'll see if we can get him going, get him enough snaps in preparation to be available to us," coach Mike Tomlin said Tuesday.
Pouncey, who is enjoying a superb season, will be able to go this week against New England, and Kemoeatu told the Steelers he expects to play this week, although he will be evaluated throughout the week, La Canfora reported, citing a source with knowledge of the situation.
Doug Legursky played guard and center before Pouncey returned. Starks left the game during the second half and didn't return. Jonathan Scott, normally a tackle, played that position and guard.
Pouncey, the Steelers' first-round draft pick, had not missed a snap all season until he was hurt while apparently being kicked in the shin. Pouncey makes all the offensive line's blocking calls, so having him out of the game could have proven disruptive. He felt better after getting a painkiller and was able to resume playing.
The Steelers don't have much time to get well; Tuesday was their only day off this week, and they resume practicing Wednesday.
"We've got somewhat of a laundry list," Tomlin said. "Working off a short week, it's important that we prepare smart in regards to working around these injuries. I'm sure many of these guys will be available for the contest, but they have limited preparation. We have to prepare smart with these guys."
The Associated Press contributed to this report.