Hess avoided the sin bin on Sunday but has since received a grade-two dangerous contact charge for attacking Papalii's legs in a tackle early in the Cowboys' 19-18 loss to Parramatta.
The NRL has taken a dim view of cannonball tackles in recent weeks, with Dolphins star Felise Kaufusi suspended for the hit that injured Jacob Laban in round 22.
Given the Cowboys have a bye across the final month of the regular season and won't play finals, Hess will be suspended for the rest of the campaign if he accepts an early guilty plea.
The former Queensland representative risks also missing the first game of 2026 if he takes his case to the judiciary on Tuesday night.
Jordan McLean is a leading option to join the 17 for next week's clash with Newcastle as he nears recovery from a calf issue.
"Fingers crossed he gets through the week next week and he's right to go," said coach Todd Payten.
Hess was the Cowboys' best player in a losing effort on Sunday, and his looming absence is a blow to the side's hopes of ending a poor season with some respectability.
The big man's form on return from an anterior cruciate ligament injury has been a rare bright spot for the Cowboys this year.
"I was surprised he wasn't considered for Origin this year, considering they (Queensland) made some changes after the first game," Payten said.
"If he continues this form, in another 12 months he should be in the mix."
North Queensland have dropped from semi-finalists last year to 14th on the ladder with a month before finals, with Payten's job under increasing scrutiny.
The coach lamented another loss for the Cowboys that consigns the side to the bottom four heading into round 24.
"It was a bit of a roller-coaster, disappointed obviously," he said.
"(After being) 18-8 down, really pleased with how we responded there and got to 18-all and fought really hard until the end but just fell short."
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