Avalanche executive vice president of hockey operations Joe Sakic and coach Patrick Roy, who is also vice president of hockey operations, made that clear during a news conference Thursday at Pepsi Center.
Stastny, who is coming off a five-year contract that paid him $6.6 million per season, will be eligible for unrestricted free agency July 1. O'Reilly, a restricted free agent, signed a two-year, $10 million offer sheet tendered by the Calgary Flames in February 2013 that the Avalanche matched. He earned $3.5 million in 2012-13 and $6.5 million last season.
Sakic said he would resume negotiations with Stastny's agent, Matt Keator, early next week.
"Paul has been open about the fact he wants to stay in Denver," Keator told ESPN.com on Friday. "We will keep talking with Joe throughout the process and give them every chance to retain Paul. We will meet next week and see where things go."
The Avalanche on Sunday opted to take O'Reilly to salary arbitration following unsuccessful discussions with his agent, Pat Morris.
"It was our right, part of the CBA window that we had, to file for an arbitration hearing," Sakic said. "I talked to Pat Morris a couple times and I told him if we didn't have an agreement that was what we were planning on doing, so there's no secret there.
"We're still trying to sign Ryan. Ryan is part of our core; he's a tremendous hockey player that we want to have here. We're hopeful that we can accomplish that, but we have our structure and he falls right in with the rest of our core. Hopefully it will work out. If it doesn't, we know we'll have an arbitrator that will tell us what he'll make."
O'Reilly, 23, is coming off the best season of his career; he scored a team-high 28 goals and finished with 64 points and an NHL-leading 83 takeaways. He took one minor penalty and is a finalist for the Lady Byng Trophy that will be awarded Tuesday at the NHL Awards in Las Vegas (7 p.m. ET; NBCSN, CBC). O'Reilly had two goals and six points in seven playoff games.
The other 29 NHL teams are eligible to sign O'Reilly to an offer sheet between July 1 and 5; the Avalanche could match it or accept draft picks as compensation. O'Reilly can't be awarded less than 85 percent of his last base salary by an arbitrator, who would present him with offers of a one-year or two-year deal.
"I know his agent Pat Morris was on TV making some comments, wondering why," Sakic said of going to arbitration. "It all comes down to we have a different point of view of where the starting point is. His agent, Pat, seems to think he signed a one-year, $6.5 million deal and forgot about the $3.5 million first year. We just have a different point of view on where the starting point is."
O'Reilly is recovering from shoulder surgery and is expected to be fine for training camp in September, Roy said.
Stastny, 28, has spent all eight of his NHL seasons with the Avalanche after playing two years at the University of Denver. He had 25 goals and 60 points in 71 games last season, with five goals and 10 points in seven playoff games.
"We've had some conversations with his agent … and we're going to continue that next week," Sakic said. "He's part of our core; we're hopeful we can sign him. We have a structure, and I know he understands that. He's unrestricted, so he can start listening to offers [Wednesday]. We're going to talk next week, and if he chooses that path, he has a right to do that and see what's out there for him. We're definitely hopeful that we'll be able to keep Paul here."
The Avalanche signed several key players -- center Matt Duchene, forward Gabriel Landeskog and goaltender Semyon Varlamov -- to new contracts in the past calendar year to fit into the team's structure. Duchene is their highest-paid player with an average salary of $6 million on a five-year contract that begins in 2014-15.
"We believe Ryan and Paul should fit within that structure," Sakic said. "We don't believe anyone should be ahead of any of those guys. We believe that they're all equally important to us. We have a structure here and we believe in taking care of those core guys, and Ryan and Paul both fit in that core with our structure. We expect to do that going forward."
The Avalanche on Thursday re-signed forward Jamie McGinn to a two-year contract. It is worth $2.9 million next season and $3 million in 2015-16, according to ESPN.com's Pierre LeBrun. The 25-year-old would have been a restricted free agent.
Roy said every team in the NHL has its own salary structure, something that was true during his playing days.
"It was working like this in '85 when I signed my first contract [with the Montreal Canadiens]," he said. "It hasn't changed. I remember [general manager] Serge Savard saying, 'I can't give you this, Larry Robinson is making that.' Today, it's the same thing. You establish who's where and where, and you go inside that structure. I think it's important that any team goes that way because you lose control, and when lose control it's very difficult."
Neither Sakic nor Roy said he feels the decision to file for arbitration in O'Reilly's case has or will cause any ill will between the sides.
"From my point of view, not at all," Sakic said. "It's just a business decision. I know Ryan understands that. I know Ryan; Ryan loves the game of hockey, he loves being here. I believe he wants to stay here. When he goes on the ice, he's status quo. He will be out there early and do what he's going to do."
Roy said he's concerned only about what O'Reilly does on the ice.
"It's not a concern to me as a coach," he said. "Ryan is a businessman. When he jumps on the ice, he's going to be a hockey player. We've been using him a lot. Ryan's performing well for us. Everybody knows I like him a lot. Ryan, at the end of the year, talked to me. He wants to learn how to win. It's the perfect fit for me. The day he's going to jump on the ice, I don't see it as an issue at all."