He led the team with 9½ sacks and has 58½ in six seasons with Atlanta, a total that ties him with Chuck Smith for second place in team history.
The 31-year-old defensive end also had four forced fumbles and one fumble recovery last season. He had 13 sacks in 2010.
Last week, the Falcons re-signed free safety Thomas DeCoud and backup defensive end Kroy Biermann. Atlanta used its franchise tag on cornerback Brent Grimes. Middle linebacker Curtis Lofton also is a free agent.
Abraham's agent, Rich Rosa, did not immediately return a phone call.