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The Falcons and free agent defensive lineman Richard Seymour have been talking about Seymour coming aboard for the 2013 season, but the two sides remain unable to reach an agreement on a contract.

Seymour told Jason La Canfora of CBSSports.com that he remains open to signing with Atlanta, where he makes his offseason home, but that the team hasn’t made him an offer that he’s willing to accept. Whether or not that remains the case, Seymour said that he’s grateful to the Falcons for their interest and their discussions about a contract.

“I thank them for their efforts,” Seymour said.

Signing Seymour seems like it would fit into the Falcons’ overall approach to this offseason, one that has seen them sign other veterans and convince tight end Tony Gonzalez to return as part of an effort that wide receiver Roddy White has described as “Super Bowl or nothing.” That hasn’t caused them to open up the purse strings as wide as Seymour would like, which could change as the team gets closer to training camp or even after training camp gets underway.

There hasn’t been much other interest in Seymour around the league, so a continued gap with the Falcons could mean the end of the line for the 33-year-old former Raider and Patriot.