Payne hasn't played since the round 18 win against Adelaide due to a foot injury.
Brisbane were hoping the 24-year-old could return for their last home-and-away game against Essendon at the Gabba.
But Lions coach Chris Fagan confirmed those plans had been put on hold.
Important defenders Darcy Gardiner and Tom Doedee are recovering from ACL surgery, while fringe tall Darragh Joyce returned early from a fractured jaw and played with a helmet during the defeat to GWS last Saturday.
"I don't think Jack will play before finals," Fagan told reporters on Thursday.
"Hopefully he can play a reserves (VFL) game in the bye leading into the first week of finals.
"We'd like to get a few of our backline stocks together so that we could put our strongest line-up out come finals time.
"But you know what? We haven't made finals yet.
"It's still mathematically possible that we could miss out, so we've just got to focus on this weekend."
Brisbane will play Collingwood on Saturday - their first match at the MCG against the Magpies since losing last year's grand final by four points.
But Fagan refused to treat the match any differently despite the chance to seek revenge on Collingwood by ending their faint finals hopes and strengthening their own top-four case.
"You can build it up if you want to, but for us, it's just another team we have to play and we have to beat to finish as high up the ladder as we can," Fagan said.
"If that means it finishes their finals opportunity, then that's OK too."
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