Koetter confirmed on Tuesday that he met with Boise State officials, but declined to elaborate.
In two seasons with Atlanta, Koetter has had mixed results.
Last season's team, led by Pro Bowl performances from quarterback Matt Ryan, receiver Julio Jones and tight end Tony Gonzalez, went 13-3 and finished 10 yards shy of the Super Bowl.
This season, the Falcons are 3-10 and has been undermined by a porous offensive line, an ineffective running game and Jones' season-ending injury.
Koetter went 26-10 as Boise State's coach from 1998-2000. He was 40-34 at Arizona State from 2001-06.
Boise State is trying to replace Chris Petersen, who took the job at Washington.