Hellebuyck did not rule out re-signing with the Jets, but he also never said his goal or hope is to stay with them beyond this season.
"I have an open mind," he said. "I'm not closing the door on anywhere."
Hellebuyck said his focus is on winning the Stanley Cup and that he thinks Winnipeg can do that even though it is without two key pieces from last season, forwards Blake Wheeler and Pierre-Luc Dubois.
The Jets bought out the final season of Wheeler's five-year contract, making him an unrestricted free agent. He signed a one-year contract with the New York Rangers. Dubois was traded to the Los Angeles Kings.
"I've had the unique scenario of having time on my side to really analyze everything, and to make sure everything is falling into place how I want it to," Hellebuyck said. "I'm going to be patient."
Scheifele said he has told the Jets front office that he is open to staying.
"I've been a Winnipeg Jet for this is my 13th camp, so it's been a long time," Scheifele said. "I've enjoyed every day of it and I'm definitely open to staying."
Hellebuyck said he did not want to talk about conversations he may or may not have had yet about a new contract, saying his agent and Jets general manager Kevin Cheveldayoff can answer them.
Scheifele said he and his agent have not had any discussions or negotiations for a new contract.
"I have one year left on my deal and I'm here to focus on this team and helping this team succeed," Scheifele said. "That's really my only focus."
But trade rumors will swirl around Scheifele and Hellebuyck the longer their futures with Winnipeg remain uncertain. The 2024 NHL Trade Deadline is March 8.
On Wednesday, Cheveldayoff did not rule out the possibility of keeping both past the trade deadline and losing them to free agency if the Jets are having a successful regular season.
"I guess you evaluate it at that point in time," Cheveldayoff said. "For us, the focus on a day-to-day basis is going to be about the process, and then we will see where things go from there. We are hopeful obviously that we earn that right to be a team that's going to make some noise and that's really what we're focused on right now.
"I hope we're in that situation where those tough decisions have to be made. It is about winning."
Scheifele has played 723 games with Winnipeg and is second in Atlanta Thrashers/Jets history with 645 points (272 goals, 373 assists), including 68 points (42 goals, 26 assists) in 81 games last season.
Hellebuyck is first in franchise history in games played (445), wins (238) and save percentage (.916). He was 37-25-2 with a 2.49 goals-against average and .920 save percentage in 64 games last season.
"We still have time," Hellebuyck said. "If it drags on and it becomes a distraction than we handle it then, but as of now it's no distraction in my eyes."