Briere, 35, managed just six goals and 16 points during an injury-plagued 2013 season, one in which the Flyers failed to make the playoffs for just the second time in the last 18 seasons.
"Obviously, I'm not very happy with the way last season went," he said. "But it's also extra motivation moving forward - to prove that I can still play, and hopefully I still have a few more years."
Added Briere: "Wherever I end up, this is where I'm going to end up [living]. This is home."
Briere is a single father who lives in Haddonfield and shares custody of his three boys, ages 12, 13, and 14.
"Obviously, I'd prefer to be close to the kids," he said. "But we don't know if it's going to be an option or not at this point."
Among the things he will consider before signing elsewhere: his role and whether that team has a chance to win the Stanley Cup.
Briere said the fans made his six years with the Flyers "amazing," and that he will never forget the team's stunning run to the Stanley Cup Finals in 2010. Briere led that run, setting a team record with 30 playoff points.
He said he thinks he has two or three years left. He will become an unrestricted free agent July 5.
The Flyers went 22-48-12 and had the NHL's fewest points (56) the year before Briere arrived. In Briere's first season, the diminutive center scored 31 goals as the Flyers went 42-29-11 for 95 points - a 39-point improvement - and reached the conference finals.
General manager Paul Holmgren said he told Briere the team was going to buy him out last week and called it a "very difficult decision." Holmgren called Briere a "tremendous player, person and role model in all aspects, and for that we thank him."
Briere's $6.5 million salary-cap hit will go off the Flyers' books 48 hours after the Stanley Cup Finals end. The Flyers are also considering using a buyout on goalie Ilya Bryzgalov.
Briere signed an eight-year, $52 million free-agent deal with the Flyers in 2007. The deal was front-loaded - Briere made $10 million the first year - and the Flyers owe him only a total of $5 million for the final two years.
Under terms of the new collective bargaining agreement, the Flyers will pay Briere two-thirds of his remaining contract, or a total of $3.33 million.
Briere, who had 124 goals and 283 points in 364 games with the Flyers, said Holmgren broke the news to him "with a lot of class, and I'll always be grateful for that and also my time here."
Briere is second player in team history with nine game-winning playoff goals, one behind Rick MacLeish.
"I have no regrets," Briere said. "I'm moving forward."
Contact Sam Carchidi at firstname.lastname@example.org. Follow on Twitter @BroadStBull.