"We will know the morning of the game whether he can play or not," Burke said Tuesday after the team's No. 1 receiver last season did not attend practice.
The CFL's outstanding rookie in 2012, Matthews is nursing a minor ankle injury sustained during Sunday's practice.
But Burke was a little more optimistic Tuesday than he had been earlier about Matthews' prognosis.
"Right now, I would say it's closer to him playing than not playing," he said. "It depends on how fast he can heal up in the next 48 hours."
If he can play, missing a few days of practice won't hurt Matthews performance, Burke said.
Receiver Terrence Edwards, who had off-season foot surgery, will be on the field.
"I'm really surprised at how well he's moving," Burke said of the veteran, who also topped the 1,000-yard mark last season for the fifth time as a Bomber.
"Last week I was going 'I don't know if he's going to be ready,' and this week he looks great."
Burke says he feels the offence is ready but he has had questions this season about his defence.
"I feel better about our defence," he said after practice Tuesday.
"I still think . . . because we have a couple of young guys there that haven't played a CFL game, I'm a little concerned for them."
On defence, the Bombers have rookies Desia Dunn, a linebacker who could be a starter with Johnny Sears still out, defensive back Marty Markett and defensive end Freddie Harris.
Burke says rookies can make their first game a bigger event that it should be and he's going to remind them they don't have to win it all by themselves.
Despite a new look offence and new protection schemes to try and keep quarterback Buck Pierce out of harm's way as much as possible, Burke says the opposition Thursday is much more of a blank slate.
The Montreal Alouettes have a new head coach and a new defence this season.
"They didn't show much in pre season. What we did see was different than what Montreal did under Marc Trestman and certainly different than what (Jeff) Reinebold did last year on defence," said Burke.
"We have no idea what they're doing and they know what we're doing."