The rookie quarterback has not practised since injuring his knee during the team's win over the Minnesota Vikings earlier this month.
Head coach Doug Marrone told the team's website: "He has thrown the ball moving-wise and we're just working as hard as we can.
"I think that if he's back by Wednesday of this week he'll have an opportunity [to play in the first game of the season] depending on how he looks on Wednesday. If he's not back by Wednesday I'm not going to look to play him in the first game.
"We'll know day by day how it's coming. Right now I don't want to give the wrong impression. Everything right now is progressing well and Friday will be a big day for him out there. Then there's a day off. Then Sunday and Monday will be big days."
The Bills play the New England Patriots in the first game of the regular season.