Murray revealed he's had discussions with Nolan about keeping him on as the team's full-time coach beyond this season.
"We're along that path," Murray said. "We have discussed the possibility of moving forward. That's all I'll say."
Following the game, Nolan declined to shed further light on the status of talks when informed of Murray's' comments.
"We'll keep it as that," Nolan said. "I won't say anything more."
Nolan is back for a second stint in Buffalo after being hired as the team's interim coach in November, when coach Ron Rolston and general manager Darcy Regier were fired. The changes were made after the Sabres got off to a franchise-worst 4-15-1 start.
The Sabres remain in last place in the NHL standings, but have shown marked improvement under Nolan, who has gone 12-19-7.
Nolan was hired by Pat LaFontaine, who took over the same day as the team's president of hockey operations. In hiring Nolan, LaFontaine said he would let the team's next GM determine whether to retain him beyond this season.
Murray was hired last month, and indicated he was open to working with Nolan.
Nolan also enjoyed a successful stint at the Sochi Games, where he coached Latvia to an eighth-place finish — the country's best in five Olympic appearances.
As for Miller, Murray said he's shopping the star goalie with the intention of trading him before the NHL's trade deadline on March 5.
"Our goal right now, I think, on both sides is to pursue a proper trade," Murray said. "The route we're looking at is to get value from him and put him in a position to succeed."
Murray said more than two but fewer than 10 teams have contacted the Sabres regarding Miller, but added it's too early to determine whether a deal can be reached.
The 33-year-old Miller is in the final year of his contract and eligible to become an unrestricted free agent this summer.
Murray said the Sabres would be interested in re-signing Miller if a deal cannot be completed.
Murray said Miller is open to being traded to a contender rather than remaining in Buffalo with a team that's rebuilding through youth.
"I don't think signing here is his first choice at his age and where we're at as a 30th-place team," Murray said. "But I wouldn't say he's got no interest."
Miller acknowledged his days in Buffalo might be numbered after he stopped 36 shots and added two assists in the win.
"I don't want to close anything off right now, but I know they're kind of looking around for an opportunity," Miller said. "And I think that's probably the best for everybody."
With the victory, Miller upped his franchise record totals to 284 wins and 540 games played. He was also the NHL's 2010 Vezina trophy-winner. That was the same year Miller earned MVP honours at the Vancouver Games, where he played a key role in leading the United States to a silver medal.
Murray is also open to shopping several other veterans who are also in the final years of their contracts. It's a group that includes captain Steve Ott, veteran winger Matt Moulson and defenceman Henrik Tallinder.