The 24-year-old speedster hasn't played since shattering his knee-cap against Canberra last August and is finally back running.
But Papenhuyzen said it would be a "miracle" if he was playing within a month as reported.
"I'm still doing testing ... three to four weeks would be an absolute miracle," he said in a post to Instagram.
"I need a good block of running, change of direction, and then back into footy skills and that sort of stuff so it's (return) still a while away.
"A goal is to make it back before the finals, and yes, will probably have to come back through Queensland Cup."
Papenhuyzen, who also endured ongoing debilitating concussion symptoms through the 2021 season, spent time in the USA with specialist Bill Knowles earlier this year looking to expedite his knee recovery.
The reconditioning specialist also worked with fellow NRL stars Latrell Mitchell and Tom Trbojevic on their injuries.
Nick Meaney has impressed in the Storm's No.1 jersey this season, with the club currently sitting fifth.
They host fourth-placed Cronulla at AAMI Park on Sunday.
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