Frawley injured a ligament in a toe on his left foot in the club's memorable win over Adelaide on Saturday evening.
The Demon failed to train and AFL.com.au spotted him in a moon boot at the club on Tuesday, raising concerns over his availability.
He was also in the boot and on crutches immediately after the Crows game.
"We think he is (a chance to play). It'll be one of those things where it'll go down to Thursday and see how he trains," Melbourne coach Paul Roos.
"He'll be touch and go and we hope that he gets up, obviously."
Roos said he and Bulldogs coach Brendan McCartney's jobs were to develop a high-level of consistency amongst their players.
"We're on a similar journey to the Bulldogs. We're training young players and getting them to do it week in, week out is very difficult," Roos said.
"We're just trying to reinforce to our players what we think makes them good players."
McCartney said his side needed to hone its ability to finish games over four quarters.
"Right now we're in games nearly all the way, but we're not closing them out and that's the next step," he said.
"We're not the only club that's ever been there and we won't be the last club to be there, but I'd much rather be in that position late, and as numbing and as disappointing as it is, at least you know you're getting closer."
McCartney also admitted his side did everything it could to lock down on Bomber veteran Dustin Fletcher, who played a critical role in stealing Saturday night's game away from the Bulldogs.
"We did try quite a few things and in the end he had an opponent. But you're talking about an all-time great who just knew where to stand," McCartney said.
Both coaches agreed their sides needed to strike a better relationship between attack and defence, but Roos made no apologies for the way his team was clamping down defensively on the opposition.
"Any coach will tell you it's about balance," Roos said.
"You want to kick more goals than you concede, but history tells you the best defensive teams are the ones that win premierships."
Both Roos and McCartney were on hand to help launch the Field of Women event at the MCG.
The Breast Cancer Network Australia is urging fans to be part of a group of 15,000 people who will stand on the MCG to form the shape of the Pink Lady before Saturday's game between the two sides.
Twitter: @AFL_BenGuthrie
