Gruden, younger brother of former Oakland and Tampa Bay coach Jon Gruden, said his interview Thursday at Cardinals headquarters was his first for a head coaching job with any NFL team. He said he might interview with the Philadelphia Eagles next week.
Arizona is seeking a replacement for Ken Whisenhunt, who was fired after six seasons.
Gruden met with Cardinals president Michael Bidwill, newly named general manager Steve Keim and player personnel director Jason Licht.
"You can tell how passionate they are about the game, how much they want to win and bring this team back to where they were with Kurt Warner," Gruden said. "The passion and drive is there. Now it's just a matter of maybe bringing in something new, some new ideas to try to get that thing done."
Gruden, 45, has extensive experience in the Arena Football League, including two stints as head coach of the Orlando Predators from 1998 to 2001 and from 2004 to 2008. In 2002 and 2003, he returned to the team as quarterback.
He worked on the staff of his brother at Tampa Bay for seven seasons, while during some of that time continuing his Orlando Predators duties.
"I've been a head coach before for a while," Gruden said. "I know it's a different league and it's not the NFL, but I've handled people and handled organization, handled salary caps, done all the things necessary to be a head coach. I understand the game and I think it would be a good fit."
He said he turned down chances to interview for head coaching jobs a year ago.
"It was my first year last year as a coordinator," Gruden said. "The Brown family gave me an opportunity to be an offensive coordinator. I didn't want to jump ship after the first phone call. I wanted to go in there and see Andy Dalton progress another year, see A.J. Green progress another year, see what we could do."
He said his brother had offered some worthy advice to him going into his first head coaching interview.
"Jon's always got his two cents to add. He can talk with the best of them," Gruden said. "And he's been around the block a few times. He's been to interviews and knows how the process works and been a big help. So I picked his brain a little bit and he's been excellent in the process, as usual."
Copyright 2013 by The Associated Press