Not quite a "must-win" game for the seventh-placed Broncos, the pressure is nevertheless on to break a worrying four-game losing streak and cement a finals appearance.
After hosting the Storm, the Broncos battle Manly at Brookvale and then Penrith at home over the remaining rounds of the regular season.
Parker did enough contact work at training on Wednesday to suggest he was a chance of being a late inclusion to line up against Melbourne but not enough to show he was a certainty to play.
To onlookers, it may have seemed good enough but coach Anthony Griffin will adopt a conservative approach rather than risk losing Parker for the rest of the season and possibly the finals.
"We'll make a decision on Thursday but if you noticed he didn't do a great deal of contact work," Griffin told AAP.
"He's keen to go, he always is but you have to be smart about what's right for him and for the team."
A renowned fast healer, Parker was expected to miss between two to three weeks after suffering ligament damage to his left shoulder against Canberra less than a fortnight ago.
"Corey knows his body and he's had a few injuries lately so we'll take a lot of notice of what he thinks along with our medical team who have been treating him before we make a final decision," said Griffin, not overly confident about his chances.
Griffin was, though, full of praise for how Josh Hoffman handled his axing last week after turning up late for training.
Hoffman hasn't claimed back his fullback spot from Corey Norman but Griffin has found a place for him on the wing at the expense of promising youngster Lachlan Maranta.
"It was a difficult decision but one that's best for the team," said Griffin.
"Corey played very well against the Bulldogs, scoring a try and he probably should have scored another one.
"It wasn't an easy decision but for the moment I just want to hang with it and see how it goes.
"Josh did very well accepting a tough decision last week. He played very well for Redcliffe so it would have been hard to leave him out after he showed he was busting to get back in the side."
Brisbane football manager Andrew Gee said young prop Josh McGuire was only likely to miss one week after coping an accidental poke in his left eye against the Bulldogs.
McGuire sustained a detached retina in round eight against the Bulldogs last year and required a five-hour operation to restore his vision.
But Gee said he had burst a blood vessel in his eye and was only expected to miss one week.