Brown suffered a mild concussion after a hit to the helmet early in the first quarter against Marshall last week. He did not return to the game.
The fifth-year senior returned to practice Tuesday with the first-string offense and went through Wednesday's practice with no ill effects, Stewart said. But the team will continue to monitor him throughout the rest of the week.
If Brown can't play, true freshman Geno Smith would make the start. Smith was 15-of-21 for 147 yards and a touchdown in relief of Brown during West Virginia's 24-7 win over Marshall.
The Mountaineers are 5-1 overall, 1-0 in the Big East.
Brian Bennett covers Big East football for ESPN.com.