The sides have more talks planned, according to a league source, and are deep into discussions for Hawk, the fifth overall pick in the 2006 draft, to remain a Packer.
Hawk was released to avoid a $10.5 million escalator in his contract, but he remains interested in staying in Green Bay, and the Packers would like to keep him prior to him having the chance to hit the open market.
There was a report Wednesday night by Milwaukee television station WTMJ-TV, citing two sources, that Hawk is set to sign the new deal Thursday at Lambeau Field.
"With A.J., the business side of the game is driving this decision," Packers general manager Ted Thompson said in a statement announcing Hawk's release. "We're hopeful that we can continue to work with A.J. to have him be a part of our team in the future."
Hawk was one of three players the Super Bowl champions let go Wednesday, along with tight end Donald Lee and safety Derrick Martin.
Lee was set to earn $2.2 million in 2011, and Martin was slated to make $750,000.
Hawk has not missed a regular-season game, making 77 starts in his 80 regular-season games.
The Associated Press contributed to this report.