Nothing is imminent, one of the sources said.
Bennett, 32, signed a three-year extension in December 2016. The contract has three years remaining, with base salaries of $1.65 million, $6 million and $7.5 million. ESPN's Brady Henderson reported last week that the Seahawks were open to trading Bennett.
The Falcons need an established pass-rusher, especially on the interior of the defensive line, with Dontari Poe gone after one season and the team cutting Derrick Shelby. Also, Adrian Clayborn, who led the Falcons with 9.5 sacks last season, is bound for free agency and expected to sign elsewhere. Bennett had 8.5 sacks and 24 quarterback hits last season and has 54 career sacks.
There is a natural tie between Bennett and the Falcons. Coach Dan Quinn used to be the defensive coordinator and defensive line coach in Seattle and has a close relationship with Bennett. Defensive coordinator Marquand Manuel used to be a defensive assistant in Seattle and has close ties to Bennett as well.
The parameters involved in such a trade are unclear. The last time the Falcons traded for a veteran starter, they surrendered two sixth-round picks to Tennessee for left guard Andy Levitre.
In a recent trade for a pass-rusher, the Dolphins acquired Robert Quinn by sending a midround pick to the Rams, likely a third- or fourth-rounder, a source told ESPN's Adam Schefter. The Rams and Dolphins are also swapping late-round picks.
The Falcons entered the offseason intent on bolstering their offensive and defensive lines. They have two exceptional young edge-rushers in 2016 sack champ Vic Beasley Jr. and Takk McKinley, plus a budding superstar in nose tackle Grady Jarrett. Bennett could help solidify an athletic, fast defense that ranked in the top 10 in both yards allowed and scoring last season.
Bennett is known to be outspoken and took a stance against social injustice by sitting during the national anthem. Those who have played with him and coached him say he is a great teammate.
Bennett is represented by Doug Hendrickson, the agent who represents Falcons general manager Thomas Dimitroff.