This is just a curious note, but I wonder how the Cardinals decide on a head coach?
Conjecture on my part - I'm assuming this organization is not far enough along in sophistication to delegate entirely to the GM (in this case Graves).
So what probably would happen (and probably has in the past) is Mr. B (and possibly one or more of his sons and others they trust) "ask around", keeping the circle of people they seek advice from as small as possible - relying solely on those they feel they can trust.
After that, it probably becomes a function of family members (and probably the GM and close trusted associates like Guilfoyle sitting down periodically to develop (and then pare down a short list) and then discreetly bring in candidates for the job.
If they're interested in contacting candidates who are currently employed in the NFL, they have to wait until the season is over for any team. (I suspect that if it's a college coach, they have to respect NCAA tampering guidelines as well).
This can slow them up considerably, and also put the team in a position of "having to compete" with other disgruntled teams for head coaching talent. (Several years back, Mike Holmgren was rumored to be on the Cardinals' short list, but he opted for a cushier job for Wolf at Green Bay and is now doing well at Seattle). So imagine if we ended up in a pissing contest with the Giants (who are rumored to be disatisfied with Fassell) for the opportunity to sign Stoops or Mularkey.
Final point - Despite Jim Fassel's struggles this year (mainly due to Accorsi's failure to rebolster his team's offensive line), I'd hire him in a heartbeat if he became available. He's been here. He has Mac's intensity, but also is a bright offensive mind who understands QB's and isn't afraid to pull the trigger on decisions earlier rather than later.