Neither Parker (strained medial ligament) or Norman (groin) took part in Thursday's extended training session and both will need to convince coach Anthony Griffin of their fitness by Sunday morning.
Norman, whose recent form, along with halfback Peter Wallace, has come under the microscope since their impressive early season efforts, was absent from Red Hill. He instead attended a pool session in a bid overcome his niggling groin injury.
"I haven't run yet, I've only done cross training," said Parker who recently made a swift recovery from a badly gashed shin.
"I'll have a run tomorrow and see how it pulls up and I will know more then.
"I want to play but I've obviously got to make a calculated decision about playing and the risk of hurting it more and potentially missing all of the season."
The bonus for Brisbane was utility Ben Te'o's successful visit to the judiciary on Wednesday night with his downgrade allowing him to play against the Eels.
If Parker can't play, Te'o, who made his State of Origin debut earlier this month, will come straight into the starting pack.
Brisbane will have their final training run on Sunday and both Parker and Norman would be expected to run at pace if they are to play.