According to two league sources, the Falcons could offer the job to Heckert as soon as this weekend.
Further driving the speculation that Heckert will be taking the Falcons job is that Atlanta has asked the Giants for permission to interview former Eagles assistant and current Giants defensive coordinator Steve Spagnuolo. It's widely believed that if Heckert were the Falcons' GM he'd want Spagnuolo as his head coach.
The Giants have declined the Falcons' request to interview Spagnuolo ahead of their game against Dallas this weekend. However, the word is that it's just a temporary no and that if the Giants were eliminated from the playoffs this weekend Spagnuolo would then interview for the job.
Spagnuolo has brought the Eagles style Jim Johnson attacking defense to New York and had great success with it. So, if we were to lose Heckert it would likely end up being a net gain if he pilfered Spagnuolo from the Giants.