Schefter reported the Lions are one of four teams to request to talk with Gruden, the brother of ESPN analyst and former Tampa Bay coach Jon Gruden, joining the Titans, Vikings and Redskins.
Gruden fits the profile of what Detroit is looking for in its next head coach. He has head coaching experience, albeit at the Arena Football League and United Football League levels, but was successful in the AFL, winning two league titles.
He is an offensive mind, having run the Cincinnati offense since 2011, and helped develop quarterback Andy Dalton over his first three seasons. Dalton is a 60.9 percent career passer with 11,360 yards, 80 touchdowns and 49 interceptions during his first three seasons.
The Bengals were the No. 10 offense in the NFL this season in yards per game, but were 20th in 2011 and 22nd in 2012. So there is some question about his productivity there.
"Jay has done an incredible job with Andy but also with implanting all of our young players and to me, that's where we are in the NFL right now," Cincinnati coach Marvin Lewis said in October. "You've got to interject the young guys, you can't draft them and have them stand behind us. We have to get them in there, get them going and making them productive."
Gruden would be an interesting choice for the Lions, who have appeared to make head coaching experience a priority for them during this cycle because the team believes they have the pieces in place to win now, just with some fine-tuning.
The 46-year-old Gruden played college football at Louisville, where he was a quarterback. He then played in NFL Europe and in the Arena League. Other than Cincinnati, his other NFL experience came with Tampa Bay, where he worked under his brother, Jon.
He split time between coaching and playing in the AFL from 2002 to 2008 while also coaching with the Bucs, according to his bio on the Cincinnati website.
He is the second candidate to officially surface with the Lions, joining Baltimore offensive coordinator Jim Caldwell, who interviewed with the team Friday.