The Storm are also confident sealing their star fullback's signature won't prove a block to contracted young gun Sualauvi Fa'alogo.
Papenhuyzen, contracted for next season, is one of the highest-profile players on the open market for 2026.
But the 26-year-old will reportedly shun interest from Canterbury to extend that deal.
"It's in a positive position where we're getting more and more confident in Ryan extending with us. We're working through those details," Storm chief executive Justin Rodski said.
"At the moment, there's a couple of different options on the table that we're discussing, but at this point in time we're getting more and more confident that he'll remain in Melbourne and extend his contract with us."
Rodski indicated a one-year extension through to the end of 2026 was the most likely of those tabled.
"I think that that's a great option for both club and player, and it gives us all another at least two years with Ryan Papenhuyzen wearing the Melbourne Storm jersey," he said.
Rodski was confident it wouldn't just be kicking the can down the road in regards to the "invested" Papenhuyzen's future and wouldn't rule out a longer-term deal in a year's time.
A role change doesn't appear on the cards.
"He knows that and I think we all know that Ryan Papenhuyzen in full flight is our starting fullback," Rodski said.
"We're pretty confident, off the back of the finish to the season that we've just had, that he'll come back at full strength, he'll have his full pace back, and it's going to be really exciting for everyone to see.
Fa'alogo, 21, is contracted until the end of 2028 but may have to play on the wing or come off the bench to earn valuable playing time.
"Sua's obviously an up and coming star of the competition," Rodski said.
"He's on a long-term contract with us.
"We're going to have to work through what positions he can play. We want him to be playing as much first-grade as possible.
"You never know what's going to happen. You never know what's going to happen with injuries. You never know what's going to happen with other positions.
"But I can guarantee that we'll be doing everything we can to see more of Sua in 2025 and beyond."
The Storm have ruled out a loan deal for next year.
They previously sent Harry Grant on loan in 2020 as part of a swap deal with Wests Tigers for Paul Momirovski.
"We've always got everything on the table, and that's certainly an option in the future," Rodski said.
"It won't be for 2025 but whether it is for 2026 and beyond, is something that we'll sit down and explore at the right time, but there's a lot of water to go under the bridge before we even entertain that."
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