Per PFT:

At a time when rumors continue to circulate that Stephen Ross might soon acquire control of the Dolphins from Wayne Huizenga, which would then allow V.P. of football operations Bill Parcells to walk away with pay, Parcells made an appearance on Monday at the Senior Bowl in Mobile.

Parcells was spotted with G.M. Jeff Ireland and coach Tony Sparano. Jeff Darlington of the Miami Herald called it the “Tuna Trifecta.” (We prefer the “Tuna Trinity.”)

But Parcells, who per Darlington didn’t travel to any of the team’s road games in 2008 and was seen only one time at the Senior Bowl in four years as the coach of the Cowboys, wouldn’t comment on the reason for his presence.

”I don’t talk. He does the talking,” Parcells said, pointing at Sparano.

A cynical mind might think that Parcells wanted to be seen (even if not heard) in order to generate interest in purchasing his services if/when he walks away from the Dolphins with the balance of his contract in hand.

Amid rumors that perhaps he wants to coach again and given that his son-in-law, Scott Pioli, could soon be looking for a head coach in Kansas City, we won’t rule out at this point the possibility of Parcells wearing a big red sweatshirt next season.
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I can't see Parcells taking a position as a HC where he didn't have control over personnel again. I'm sure the Dallas fiasco left a bad taste in his mouth. That being said, Pioli said during his press conference that his accepting the Chiefs job wasn't about him trying do it on his own. If you take him at his word, he may not be opposed to allowing Parcells to take control of personnel in the same manner Belichick did in NE.