Miller, a former Vezina Trophy winner as the league's top goaltender, and Vanek, Buffalo's top offensive threat, reported for physicals Wednesday after an offseason filled with trade speculation.
Both players are in the final year of their contracts and are not currently negotiating extensions with the Sabres.
"If you play long enough, you're going to have this type of discussion surround you at some point," Miller said. "I have to be professional enough just to do the job. I'm able to do a job in a city I'm familiar with, a city I'm very much at home. I like to be in Buffalo. I like the people.
"So this isn't a bad situation."
General manager Darcy Regier said the window for making training camp deals has closed, but that talks will heat up again as the in-season trade deadline approaches.
Regier did shore up his roster on another front later in the day, re-signing restricted free agent Cody Hodgson to a multi-year contract. Hodgson is Buffalo's top-line center, who finished last season second on the team with 15 goals and 34 points in 48 games.
The Sabres are in transition. They opened last season with Stanley Cup aspirations, but have since elected to rebuild an under-performing roster with prospects and draft picks after missing the playoffs for a second straight year.
Miller acknowledged at the end of last season that he may no longer fit into the Sabres' long-term plans.
Following last season's home finale, Miller skated a lap around the ice, waving to fans. He also sold his home over the summer and is now renting.
"It does look like, `OK, I'm out of here," Miller said. "People are going to believe it or they're not going to believe it. I thought it was a smart business decision to have it on the market in the last year of my deal so I didn't at least get low-balled.
"I had to laugh at myself and say, `this is not going to be looking good to the people of Buffalo.' I'm not racing out of town. It was just honestly a business decision."
Vanek has previously said he is not interested in enduring a lengthy rebuilding process and will take this season to assess. On Wednesday, he was more political.
"I'm not ready to re-sign, and to be honest, I'm not sure if they are ready to re-sign," Vanek said. "If I would have got traded, I wouldn't have been shocked."
Regier said the NHL's new collective bargaining agreement has made players with expiring contracts reluctant to sign extensions.
"That's the nature of the new NHL," Regier said. "The expectation from the players side is that the cap is going to go up. To the extent that the cap goes up, it may be beneficial for them to wait for the unrestricted market."
Miller, who has played 500 games with the Sabres, left the door open to re-signing long-term.
"You start to see a situation here where you can build something good, something that's going to last," Miller said. "That's what I want to be a part of, whether this is the last season I can make a difference or it's going to continue forward. I just want to make sure that I'm a positive influence on this team moving forward and that Buffalo has a lot of success or a foundation to build success on in the future, because I do care about this area and the people. I do believe they deserve to be cheering for a team deep into June.
"My hope is that we can do that this year."
Hodgson is part of that foundation. He's a fourth-year player, whom the Sabres acquired in a trade with Vancouver in February 2012.
We feel he is going to be an important piece of our organization's success," Regier said in a statement released by the team.
Regier said he's also had preliminary discussions with the agent for forward Steve Ott about a contract extension. The veteran center, acquired in a trade from Dallas last offseason, is in the final year of his deal.
"I want to be here," Ott said. "I love the organization, the sense of where it's going, the young guys, the stable full of prospects. As you add pieces and continue to build the team, I see the uphill climb beginning very shortly."
NOTES: Coach Ron Rolston completed his staff by hiring former Harvard assistant Jerry Forton, a Buffalo native who has also worked at UMass-Lowell and Niagara. . Rolston said he will choose his captains at the end of training camp after rotating the captaincy for preseason games. . The Sabres will hold their first on-ice session Thursday and play their first preseason game Sunday in Montreal. ... Buffalo opens the regular season at Detroit on Oct. 2.