The Giants said that Smith met with team president John Mara and general manager Jerry Reese on Monday.
Smith is the sixth person to interview for the job that opened a week ago when Tom Coughlin stepped down after 12 seasons.
Giants offensive co-ordinator Ben McAdoo and defensive counterpart Steve Spagnuolo were the first two to interview. Jacksonville assistant and former Buffalo coach Doug Marrone, Lions defensive co-ordinator Teryl Auston and Bears offensive co-ordinator Adam Gase of the Chicago Bears also interviewed.
Gase was hired as the Miami Dolphins’ coach on Saturday.
The 56-year-old Smith coached the Falcons from 2008-14. He was 66-46 in the regular season and 1-4 in the post-season, including a 24-2 loss to the Giants in a 2011 NFC wild-card game.
In his first five seasons, Smith’s Falcons were 56-24 (.700), won two NFC South titles and earned four post-season berths. Atlanta advanced to the NFC championship game in the 2012 season, but lost to San Francisco, 28-24.
Smith was the first coach in Falcons’ history to produce back-to-back winning seasons (2008-09), and he was the first Atlanta coach to lead the team to three consecutive playoff appearances (2010-12). He was 10-22 in his final two seasons.
Smith has coached for 33 seasons, including 16 in the NFL. Prior to joining the Falcons, he was the Jacksonville Jaguars defensive co-ordinator from 2003-07.
