The 150 acres east of the airport would be a great site, Clayton County Commission Chairman Jeff Turner said told The Atlanta Journal-Constitution.
"We want to make sure they know we're interested," Turner said. "If they can't work out a deal in Atlanta, Clayton is interested in entering into discussions in how we can bring the stadium to Clayton County."
The team's current lease with the Georgia Dome downtown is nearing an end, and team officials say they prefer to build a new stadium instead of making improvements to the dome.
Falcons spokeswoman Kim Shreckengost said the team has not been contacted by Clayton County and is not familiar with Turner's idea. She said the Falcons remain focused on working with the city of Atlanta to reach an agreement on a downtown stadium.
State and local officials are considering plans to use a special hotel tax to help finance a new retractable-roof stadium in downtown Atlanta.
Falcons President and CEO Rich McKay has told the Atlanta City Council that the team would have no choice but to consider other sites if negotiations on the downtown Atlanta site break down.
It's not the first time the team has raised the specter of leaving downtown. However, McKay told the city council that this time, the idea is not a threat -- and the team intends to have a new stadium somewhere by 2017.