The Storm announced on Friday that Papenhuyzen had inked a new contract extension to remain in Victoria until the end of the 2025 season.
The decision followed the retention of supercoach Craig Bellamy, who will enter a 20th campaign next year in leading the Storm from his coaching post.
Bellamy will take up a directors role with Melbourne after the 2022 season, while also leading the pursuit to find his successor.
The mastermind coach's re-signing was a key factor in Papenhuyzen committing to the club for a further three seasons as the Storm look to continue their 21st century dominance.
With a bevy of superstars already signed for the long haul, Smith frames as one of the missing pieces to the next Storm dynasty puzzle.
The New Zealand international is currently contracted to the club until the end of next season, but is sure to gain surging interest from rival clubs should he remain unsigned come November 1.
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The Roosters are the latest club to show interest in the gun dummy-half, while the Bulldogs, Tigers, Broncos and Titans have expressed their desire in the past.
Smith was granted to pursue an early release from the final year of his contract last December, a decision the Storm have since looked to backflip on.
With the club now a strong chance to retain their cult hero, Papenhuyzen has backed Smith to sign on the dotted line and join his teammate in their venture for further success.
“It would be a massive signing if we could get the Cheese (Smith) and hopefully he’s got the same mindset as me,” Papenhuyzen said, per The Daily Telegraph.
“The group is sort of formed now and it would be pretty special if he was to sign on as well.
“And with Bellza (Bellamy) re-signing, hopefully a lot of players will see that and want to come to the Storm.
“And I know Bellza and Cheese have a pretty good relationship and it’s a bit of a love-hate one, so hopefully he can sign and make that happen.”
The Storm's push for premierships past this season will be hindered by the departures of Dale Finucane (Cronulla), Josh Addo-Carr (Canterbury), Nicho Hynes (Cronulla) and Brenko Lee (Brisbane) at this year's end.
With Harry Grant set to man the No.9 jumper, Smith has been utilised further forward and could be the club's answer to replacing the departing Finucane.