However, Grimm said Tuesday that no interview has been scheduled. He said the Bills are working through his agent, Eric Metz, and he doesn't know if any talks will materialize.
"I don't know what the time schedule is on that," Grimm said. "I'm not really worried about it right now. I've got a few important things to take care of first."
The Cardinals are preparing for Saturday's NFC divisional playoff game at New Orleans.
"It's always flattering when you're considered for it," Grimm said of the Bills' interest, "but you've got to wait and see what it all contains and pertains to and how it's run -- but that's all down the road."
"Russ and I have been together a long time," Whisenhunt said. "We played together and we coached together. I think he's certainly well-deserving of an opportunity. He has all the characteristics you want to see in becoming a head coach, and I certainly hope he does get his chance, which I feel he will."
Grimm made four consecutive Pro Bowls as an offensive guard for the Washington Redskins, helping them win three Super Bowls. He is a finalist for the Pro Football Hall of Fame for the fourth consecutive year.
The Bills also have asked for permission to interview New York Jets offensive coordinator Brian Schottenheimer, a source told The Associated Press on Monday. It's unclear when the interview might take place, said the source, who spoke on the condition of anonymity.
The Associated Press contributed to this report.