Elliott left the Bulldogs at the end of the 2021 season in ugly circumstances, before ultimately signing a career-saving one-year deal with the Canberra Raiders.
He has turned himself into a versatile forward for the club, with the strong back rower starting the last couple of games at hooker.
He was due to do the same again during Magic Round against the Cronulla Sharks on Sunday afternoon, however, was ultimately ruled out 24 hours before kick-off.
Speaking to reporters on Friday though, Stuart said he is keen to keep Elliott at the club for the long haul following a string of impressive performances to start the season.
"Adam knows where I stand with him in regards to the long-term," Stuart said.
"Yes, I want to keep here, and talks with [NRL Recruitment and Pathways Manager] Kelly Egan and [Elliott's manager] David Riolo are all very healthy at the moment, so I'm very confident that will be the case.
"It's just a matter of tying up a few bits and pieces to their communications of the deal."
Elliott is an experienced NRL forward at this point, and has been one of Canberra's better players during their early-season struggles.
His form comes after speculation before the season started that he may not have even had a spot in the starting 17 for Canberra.
Stuart said he had been impressed with how Elliott had played in the second row, while also confirming that Elliott is pushing for a permanent spot in the starting pack.
"He doesn't just fill in, he does a good job there," Stuart said of the former Bulldog ahead of their NRL Magic Round clash in Brisbane on Sunday with the Cronulla Sharks.
"It's difficult for a backrower to go into nine, but it shows his utility value in being able to sustain some time there. He's doing a really good job for us in these difficult times."
"Adam Elliot is definitely pushing for a spot in the starting pack, whether it's at nine, 13, or on the edge, and that's what I want.
"I want people to fight for spots. We haven't got enough of that at the moment in certain positions, and I've always said as a coach I love having people fight and compete for positions."