The former Queensland prop extended his contract with the Green Machine for one year after they claimed the minor premiership last season, but hopes of the 34-year-old continuing with the club have been dashed.
When asked on Friday if Papali'i would stay in the nation's capital, Stuart said: "No, he won't be."
"You don't want to lose the investment we put into players like Josh ... We have a lot of young Polynesian boys in our club as well, and I know they look up to Papa as though he's their god," the coach added.
"He's seen as that leader and guy who's done it on the field, not through talk, but through action.
"But at the moment, we're thinking short term. We've really missed Josh, and getting him back will be a big bonus."
Papali'i is currently sidelined with a calf injury picked up in April, but the loss of Canberra's most-capped player will be felt even more next season, especially after having played his first game for the Raiders as a teenager in 2011.
The 34-year-old has not only enjoyed success with the Green Machine, but also excelled in the State of Origin arena.
He has made 24 appearances for the Maroons and came out of Origin retirement last year to help the Queenslanders secure a fairytale series victory.
But Stuart is currently focused on Saturday's clash against Parramatta and helping the Raiders rebound from a sloppy 26-0 thumping by the Sydney Roosters last Friday, which he labelled their "worst game of the season".
Despite the losses of second-rower Hudson Young and five-eighth Ethan Strange to Origin, and winger Savelio Tamale (concussion), the coach is remaining upbeat, especially as prop Vena Patuki-Case is set to make his debut from the bench.
"I think the character (Patuki-Case's) speaks for itself. He's had multiple leg injuries, from syndesmosis to fractures, and I give him credit for actually still being around," Stuart said.
"We read in all the textbooks and everything in regards to resilience or being mentally tough, and we're seeing it first hand with Vena.
"If anybody deserves a debut and the Raiders jumper, it's Vena."
Captain Joe Tapine will also celebrate the occasion as he plays his 250th match and he's hoping the milestone can help the Raiders continue their 9-0 streak of beating teams after scoring zero points the round before.
"I just want to get the win for Vena first. You remember your first game more than your 250th," Tapine said.
"250 sounds like a long time. It's been 13 years. I've obviously got a couple more years in me and will try to play as many games as I can for this club."
Parramatta will be without Mitch Moses, also on Origin duty.
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