The interview is expected to be conducted on Monday.
Tom Coughlin stepped down Monday as head coach after 12 seasons with the Giants and a 102-90 record, including 8-3 in the playoffs with two Super Bowl victories.
Smith went 66-46 with the Falcons from 2008-14, leading the Falcons to the playoffs four times.
The Giants have interviewed Giants offensive coordinator Ben McAdoo and defensive coordinator Steve Spagnuolo. The team was scheduled to interview former Buffalo Bills head coach Doug Marrone, now the Jacksonville Jaguars' offensive line coach, on Saturday.